=Paper=
{{Paper
|id=Vol-2783/paper00
|storemode=property
|title=The Scientific Contribution of Nikolai D. Botkin
|pdfUrl=https://ceur-ws.org/Vol-2783/paper00.pdf
|volume=Vol-2783
|authors=Varvara Turova
|dblpUrl=https://dblp.org/rec/conf/birthday/Turova20
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==The Scientific Contribution of Nikolai D. Botkin==
https://ceur-ws.org/Vol-2783/paper00.pdf
The Scientific Contribution of
Nikolai D. Botkin ?
Paris, 1993.
The workshop “Mathematical Modelling and Scientific Computing: Focus on
complex processes and systems” held on November 19-20, 2020, at the Technical
University of Munich, was dedicated to Nikolai Dmitrievich Botkin who passed
away on September 14, 2019. In this article, we give a short description of the
most important scientific results and a complete list of his publications.
Nikolai Dmitrievich Botkin was born on March 22, 1956 in Sysert, Sverdlovsk
Region (USSR) to the father Dmitrii Sergeevich Botkin who taught mathemat-
ics and the mother Matrena Samuilovna Afanasenko who taught physics. After
graduating from the Faculty of Mathematics and Mechanics of the Ural State
University in Sverdlovsk, he was employed in the Dynamical Systems’ Division
of the Institute of Mathematics and Mechanics of the Ural Branch of the USSR
Academy of Sciences (Sverdlovsk).
The scientific research of N. D. Botkin during the period of his work at the
Institute of Mathematics and Mechanics (from 1978 to 1992) was devoted to the
theory and numerical methods of differential games. Nikolai Botkin obtained
theoretical results in the field of positional optimal control and constructing
value functions [4], [5], [8], [10], [199], [200], [207], [216], a posteriori estimates
?
Copyright c 2020 for this paper by its author. Use permitted under Creative Com-
mons License Attribution 4.0 International (CC BY 4.0).
ii
for the numerical construction of solutions to differential games [3], [6], [77], [139],
[141], and developed the first algorithms for calculating stable bridges in linear
differential games [12], [76], [82], [106], [146], [201], [203], [204], [209], [211]–[214],
[218], [219].
At the age of 27, in 1983, Nikolai defended his PhD thesis “Numerical so-
lution of linear differential games” [1], [2]. During the decade 1982–1992, the
methods developed by him were successfully applied [7], [9], [13], [16], [78]–[81],
[107], [140], [142]–[145], [202], [205], [206], [208], [210], [215], [217] to the prob-
lems of aircraft control under wind disturbances in the framework of cooperation
with the Academy of Civil Aviation in Leningrad, Russia. A method of aircraft
landing control relying on switching lines was patented [104] in 1988. In the early
90s, based on an analysis of the asymptotic behavior of solutions to nonlinear
differential games, he proposed a novel algorithm for computing the discriminat-
ing kernel of differential inclusion [11]. This algorithm was later on effectively
implemented [46] in terms of level sets, which allowed to use it for solving many
applied problems.
In 1992, Nikolai received a scientific grant from the Alexander von Humboldt
Foundation and worked for a year at the University of Würzburg, and for the
next six months at the Technical University of Munich. During this period, he
kept working on differential games [14], [83], [147], [148], [150], and was engaged
in the development of new effective algorithms in the field of convex optimization
and linear and quadratic programming [15], [17], [84], [149], [151], [152], [220],
[221], continuing this work in later years [26], [31]. In particular, a very effective
numerical algorithm for finding Chebyshev center of a finite point set in the
Euclidean space Rn was created, which is often used by researchers in various
scientific fields.
From August 1993 to January 1999 Nikolai Botkin worked at the Technical
University of Munich: until March 1994 as a Humboldt Fellow in the Division
of Higher and Numerical Mathematics, and since March 1994 as a researcher
in the Division of Applied Mathematics. In line with the scientific focus of the
Division of Applied Mathematics, which was primarily on mathematical mod-
els of complex physical processes, he completed the works on identification of
unknown parameters both of nonlinear heat conductivity equations [18], [109],
[110] and of models describing phase transitions in shape memory alloys [108],
[155], [222].
In the years 1997–2002, within the framework of the DFG-project “Adaptive
materials in real-time optimization” Nikolai was engaged in research of prob-
lems related to oscillations excited by piezoelectrics in thin plates. Along with a
theoretical study of thin plate models excited by piezoelectric patches [19], [20],
[111], [112], [153]–[156], [159], [223], [224], including homogenized variants of the
models [21], [23], [85], [86], [113], [157], [158], [160], [161], as the number of piezo-
electric patches tends to infinity, he designed and implemented active real-time
controls which provide the desired performance of flexible constructions sub-
jected to varying disturbances [87], [225]. Participation in this project continued
after moving in early 1999 to Bonn for work at the multidisciplinary research cen-
The Scientific Contribution of Nikolai D. Botkin iii
ter CAESAR (Center of Advanced European Studies and Research). For seven
and half years, he took part in numerous theoretical and applied projects. These
included:
- Nonlinear interactions in piezoelectric excited surface waves (2001–2004)
- Microbalance Array Mass Spectrometry for Proteomics (2001–2004)
- Tire Sensor (2000–2004)
- Flexible Microrobot for Scanning Electron Microscopy (2000–2004)
- Shape Memory Composites for Orthodontic Archwires (2002–2005)
- Distributed Simulation of Complex Technological Systems (2004–2006)
- Elasto-Optical Biosensor on the Nanostructural Base (2004–2006)
- Safe Production and Use of Nanomaterials (2006–2007).
The work on these projects motivated the creation and substantiation of
new mathematical models, the development of efficient algorithms and numer-
ical methods. In particular, not only was a mathematical model of an acoustic
biosensor, a multi-layered structure consisting of anisotropic piezoelectric and
isotropic layers, created [24], [114], [162], [165], [166], [169], [171], [174], but also
effective numerical methods and corresponding software [29], [118], [119], [123],
[173], [177], [181], [183], [188] for the treatment of such multi-layered structures
were developed. To take into account complex interactions with fluid of special
biostructures (aptamers) that selectively bind biomolecules, a novel homogeniza-
tion approach was elaborated [25], [27], [116], [117], [164], [167], [172], [178]. In
this method, the interaction between the bristles of the aptamer molecules and
the fluid is accounted for through an averaged material whose properties are
derived using the passage to the limit in the model as the number of the bristles
goes to infinity whereas their thickness goes to zero. It should also be noted that
his contributions led to advances in the development of experimental devices
such as the elasto-optical biosensor [45], [182], [187], the microfluidic reactor for
producing nanoparticles [184], [189], the tire sensor [170], [179], and in the mod-
eling composite materials and materials with memory [115], [120], [124], [163],
[176], [180], [186], [226], as well as other important theoretical and experimental
work [22], [28], [168].
Since August 2006, Nikolai Botkin was with the Division of Mathematical
Modeling in the Mathematical Department at the Technical University of Mu-
nich. From 2006 to 2009 he was a leading researcher in the DFG project “Math-
ematical modeling and control in cryopreservation of living cells and tissues”.
He developed and investigated models describing the processes of freezing and
thawing of living cells and tissues and ingeniously applied the optimal control
theory to the design of optimal cooling protocols that minimize the damaging
effects caused by the release of the latent heat and by delayed freezing of intra-
cellular fluid [32], [90], [185], [190], [230], [233]. N. D. Botkin was the co-author
of the patent [105] for a device for freezing dental tissues. These and subsequent
years, he also continued [35], [39], [129] his research on the numerical methods for
solving differential games, developed grid algorithms for problems with nonlinear
dynamics and state constraints [37], [40], [89], [193], [234]. He was among the
first who applied numerical algorithms for solving differential games to biotech-
iv
nological problems [237], [242], in particular, to the problem of propagation of
surface acoustic waves in mathematical modeling of an acoustic biosensor [92],
[121], [122], [162], [175], [227], [236], as well as for finding optimal protocols of
freezing and thawing of living cells and tissues [34], [38], [88], [93], [194], [228],
[231], [232].
In 2009–2012 Nikolai worked on a joint project “Modeling of CO2 seques-
tration, including parameter identification and numerical simulation” of the
Technical University of Munich and King Abdullah University of Science and
Technology, Saudi Arabia. He obtained new results in the field of mathematical
modeling of multiphase flows in porous medium, with accounting for the effects
of hysteresis [41], [42], [126], [128], [195], [197].
His active work with graduate and postgraduate students of the Division of
Mathematical Modeling is reflected in publications [30], [33], [44], [55], [125],
[198], [229], where mathematical models for hydrodynamics, phase-field prob-
lems, transport in porous media, and economic problems have been developed.
Nikolai Botkin also paid great attention to research collaboration with the
Poznan University of Technology, Poland. The joint results on inverse heat trans-
fer problems were published in [36], [52], [191], [192]. Since 2012, he has been
actively involved in a scientific cooperation with the Institute for Applied Math-
ematics, Far Eastern Branch of Russian Academy of Sciences (Vladivostok, Rus-
sia), on theoretical and numerical analysis of boundary-value problems of com-
plex heat transfer [43], [47], [49], [53], [62], [68], [132], [196], [235], [239] and
inverse and optimal control problems of complex heat transfer [48], [56]–[58],
[63], [96], [131], [238].
Since 2013, Nikolay Botkin with great enthusiasm participated in the joint
project “Mathematical modeling of cerebral blood circulation in premature in-
fants with accounting for germinal matrix” of the University Clinic “rechts der
Isar” and the Division of Mathematical Modeling. He applied the methods of dif-
ferential game theory to the problems of modeling cerebral autoregulation [50],
[67], [98], [130], [240], [241]. New models of cerebral blood circulation [60], [64],
[65], [75], including models of oxygen transport [54], [69], [71], [136], [137], [243]
in the brain were also developed and investigated with his direct involvement,
and some peculiarities of cerebral blood circulation in premature infants were
explored [70], [72], [73].
In 2015, he began work on the DFG project “Robust dynamic programming
approach for solution of flight dynamics control problems” (joint with the Insti-
tute of Flight System Dynamics, Faculty of Mechanical Engineering, Technical
University of Munich), as a leading project researcher. The algorithms for solv-
ing differential games, especially for the numerical construction of viability sets
in nonlinear problems of high dimension were further developed [46], [51], [99],
using novel parallelization technologies. This made it possible to solve problems
with a phase vector dimension of 6–7, which was previously unattainable in dif-
ferential games, and successfully apply the developed algorithms to problems
of aircraft control at the stages of runway acceleration [94], take-off [91], [100],
[102], [127], [133], [134], cruise flight [59], [61], [97], [135], and landing [95] un-
The Scientific Contribution of Nikolai D. Botkin v
der wind conditions, as well as for creating algorithms for generating dangerous
wind disturbances [66], [101], [103]. Moreover, new robust control methods were
designed [74], [100], [102], [138].
Nikolai Botkin continued to work actively until his sudden death. Many of his
243 publications are frequently requested and cited by other researchers. Numer-
ical and analytical methods he developed for linear and quadratic programming,
optimal control and differential game problems are used by theorists and prac-
titioners. Nikolai Botkin’s friends, colleagues, and students will remember him
with tenderness and gratitude.
References
Theses
1. Botkin, N. D.: Numerical solution to linear differential games. PhD Thesis.
Sverdlovsk, pp. 1–138 (1983) [in Russian]
2. Botkin, N.D.: Numerical solution to linear differential games. Author’s summary
of the PhD thesis. Sverdlovsk, pp. 1–13 (1983) [in Russian]
Papers in Peer-Reviewed Journals
3. Botkin, N.D.: Evaluation of numerical construction error in differential game
with fixed terminal time. Probl. Control. Inf. Theory 11(4), 283–294 (1982)
4. Botkin, N.D., Patsko, V.S.: Universal strategy in a differential game with fixed
terminal time. Probl. Control Inf. Theory 11(6), 419–432 (1982)
5. Botkin, N.D., Patsko, V.S.: Positional control in a linear differential game. Izv.
AN SSSR. Tech. Kibernetika 4, 78–85 [in Russian]. English transl. in Eng.
Cybern. 21(4), 69–76 (1983). https://doi.org/10.1016/0021-8928(84)90004-2
6. Botkin, N.D.: Approximation error in a linear-differential game. Avtomat. i
Telemekh. 12, 5–12 [in Russian]. English transl. in Autom. Remote Control
45(12), 1537–1544 (1984)
7. Botkin, N.D., Kein, V.M., Patsko, V.S.: The model problem of controlling the
lateral motion of an aircraft during landing. Prikl. Mat. Mekh. 48(4), 560–567
[in Russian]. English transl. in J. Appl. Math. Mech. 48(4), 395–400 (1984).
https://doi.org/10.1016/0021-8928(84)90004-2
8. Botkin, N.D.: Optimal universal strategy in a linear differential game. Differ.
Uravn. 25(9), 1475–1480 [in Russian]. English transl. in Differ. Equ. 25(9),
1029–1033 (1989)
9. Botkin, N.D., Kein, V.M., Patsko, V.S., Turova, V.L.: Aircraft landing control in
the presence of windshear. Probl. Control Inf. Theory 18(4), 223–235 (1989)
10. Botkin, N.D.: Differential pursuit game with mixed control constraints. Avtomat.
i Telemekh. 6, 12–19 [in Russian]. English transl. in Autom. Remote Control
53(6), 793–800 (1992)
11. Botkin, N.D.: Asymptotic behavior of solutions of differential games. Viability
domains of differential inclusions. Dokl. Akad. Nauk 325(1), 16–19 (1992) [in
Russian]. English transl. in Math. Dokl. 46(1), 8–11 (1993)
vi
12. Botkin, N.D., Ryazantzeva, E.A.: Algorithm for constructing a solvability set in
a linear differential game of high dimension. Trudy Inst. Mat. i Mekh. UrO RAN
2, 128–134 (1992) [in Russian]
13. Botkin, N.D., Zarkh, M.A., Keyn, V.M., Patsko, V.S., Turova, V.L.: Differential
games and aircraft control problems in the presence of wind disturbance.
Izvestiya Akademii Nauk. Teoriya i Sistemy Upravleniya 1, 68–76 (1993) [in
Russian]. English transl. in J. Comput. Syst. Sci. 32(3), 110–117 (1994)
14. Botkin, N.: Approximation schemes for finding the value functions for differential
games with nonterminal payoff functional. Analysis 14(2-3), 203–220 (1994).
https://doi.org/10.1524/anly.1994.14.23.203
15. Botkin, N.D., Turova-Botkina, V.L.: An algorithm for finding the Chebyshev
center of a convex polyhedron. Appl. Math. Optim. 29(2), 211–222 (1994).
https://doi.org/10.1007/BF01204183
16. Patsko, V.S., Botkin, N.D., Kein, V.M., Turova, V.L., Zarkh, M.A.: Control of
an aircraft landing in windshear. J. Optim. Theory Appl. 83(2), 237–267 (1994).
https://doi.org/10.1007/BF02190056
17. Botkin, N.D.: Randomized algorithms for the separation of point sets and
for solving quadratic programs. Appl. Math. Optim. 32(2), 195–210 (1995).
https://doi.org/10.1007/BF01185230
18. Botkin, N.D.: Identification of unknown parameters for heat conduc-
tivity equations. Numer. Funct. Anal Optim. 16(5-6), 583–599 (1995).
https://doi.org/10.1080/01630569508816634
19. Botkin, N.D.: Estimation of parameters of a linear thin plate ex-
cited by a piezoelectric patch. Analysis 17(4), 367–378 (1997).
https://doi.org/10.1524/anly.1997.17.4.367
20. Hoffmann, K.-H., Botkin, N.D.: Oscillations of nonlinear thin plates ex-
cited by piezoelectric patches. Z. Angew. Math. Mech. 78(7), 495–503
(1998). https://doi.org/10.1002/(SICI)1521-4001(199807)78:7<495::AID-
ZAMM495>3.0.CO;2-W
21. Botkin, N.D.: Homogenization of an equation describing linear thin plates excited
by piezopatches. Commun. Appl. Anal. 3(2), 271–282 (1999)
22. Govorov, A.O., Kalameitsev, A.V., Rotter, M., Wixforth, A., Kotthaus, J.,
Hoffmann, K.-H., Botkin, N.: Nonlinear acoustoelectric transport in a
two-dimensional electron system. Phys. Rev. B 62(4), 2659–2668 (2000).
https://doi.org/10.1103/PhysRevB.62.2659
23. Hoffmann, K.-H., Botkin, N.D.: Homogenization of von Kármán plates
excited by piezoelectric patches. Z. Angew. Math. Mech. 80(9), 579–
590 (2000). https://doi.org/10.1002/1521-4001(200009)80:9<579::AID-
ZAMM579>3.0.CO;2-2
24. Botkin, N.D., Turova, V.L.: Mathematical models of a biosensor. Appl. Math.
Model. 28(6), 573–589 (2004). https://doi.org/10.1016/j.apm.2003.10.012
25. Botkin, N.D., Hoffmann, K.-H., Meirmanov, A.M., Starovoitov, V.N.: De-
scription of adhering with saturation using boundary conditions of hysteresis
type. Nonlinear Anal. Theory Methods Appl. 63(5-7), e1467–e1473 (2005).
https://doi.org/10.1016/j.na.2005.01.044
The Scientific Contribution of Nikolai D. Botkin vii
26. Botkin, N.D., Stoer, J.: Minimization of convex functions on the con-
vex hull of a point set. Math. Meth. Oper. Res. 62(2), 167–185 (2005).
https://doi.org/10.1007/s00186-005-0018-4
27. Hoffmann, K.-H., Botkin, N.D., Starovoitov, V.N.: Homogenization of interfaces
between rapidly oscillating fine elastic structures and fluids. SIAM J. Appl.
Math. 65(3), 983–1005 (2005). https://doi.org/10.1137/S0036139903421572
28. Khludnev, A.M., Hoffmann, K.-H., Botkin, N.D.: The variational contact
problem for elastic objects of different dimensions. Sib. Math. J. 47(3), 584–593
(2006). https://doi.org/10.1007/s11202-006-0069-7
29. Botkin, N.D., Hoffmann, K.-H., Pykhteev, O.A., Turova, V.L.: Disper-
sion relations for acoustic waves in heterogeneous multi-layered struc-
tures contacting with fluids. J. Franklin Inst. 344(5), 520–534 (2007).
https://doi.org/10.1016/j.jfranklin.2006.02.026
30. Hoffmann, K.-H., Marx, D., Botkin, N.D.: Drag on spheres in micropolar fluids
with non-zero boundary conditions for microrotations. J. Fluid Mech. 590,
319–330 (2007). https://doi.org/10.1017/S0022112007008099
31. Stoer, J., Botkin, N.D., Pykhteev, O.A.: An interior-point method for minimizing
convex functions on the convex hull of a point set. Optimization 56(4), 515–524
(2007). https://doi.org/10.1080/02331930701421111
32. Hoffmann, K.-H., Botkin, N.D.: Optimal control in cryopreservation of cells and
tissues. Adv. Math. Sci. Appl. 29, 177–200 (2008)
33. Amler, T.G., Botkin, N.D., Hoffmann, K.-H., Meirmanov, A.M.,
Starovoitov, V.N.: Transport equation with boundary conditions of
hysteresis type. Math. Methods Appl. Sci. 32(17), 2177–2196 (2009).
https://doi.org/10.1002/mma.1127
34. Botkin, N.D., Hoffmann, K.-H.: Control design in cryopreservation of living cells.
Trudy Inst. Mat. i Mekh. UrO RAN 16(5), 233–240 (2010)
35. Botkin, N.D., Ryazantseva, E.A.: Structure of viability kernels for some
linear differential games. J. Optim. Theory Appl. 147(1), 42–57 (2010).
https://doi.org/10.1007/s10957-010-9706-1
36. Fraçkowiak, A., Botkin, N.D., Cialkowski, M., Hoffmann, K.-H.:
A fitting algorithm for solving inverse problems of heat con-
duction. Int. J. Heat Mass. Transf. 53(9-10), 2123–2127 (2010).
https://doi.org/10.1016/j.ijheatmasstransfer.2009.12.039
37. Botkin, N.D., Hoffmann, K.-H., Mayer, N., Turova, V.L.: Approximation schemes
for solving disturbed control problems with non-terminal time and state con-
straints. Analysis 31(4), 355–379 (2011). https://doi.org/10.1524/anly.2011.1122
38. Botkin, N.D., Hoffmann, K.-H., Turova, V.L.: Optimal control of ice formation
in living cells during freezing. Appl. Math. Model. 35(8), 4044–4057 (2011).
https://doi.org/10.1016/j.apm.2011.02.020
39. Botkin, N.D., Hoffmann, K.-H., Turova, V.L.: Stable numerical schemes for
solving Hamilton-Jacobi-Bellman-Isaacs equations. SIAM J. Sci. Comput. 33(2),
992–1007 (2011). https://doi.org/10.1137/100801068
40. Botkin, N.D., Hoffmann, K.-H., Mayer, N., Turova, V.L.: Erratum to:
Approximation schemes for solving disturbed control problems with
non-terminal time and state constraints. Analysis 32(1), 85 (2012).
viii
https://doi.org/10.1524/anly.2012.0943
41. Brokate, M., Botkin, N.D., Pykhteev, O.A.: Numerical simulation
for a two-phase porous medium flow problem with rate indepen-
dent hysteresis. Physica B Condens. Matter 407(9), 1336–1339 (2012).
https://doi.org/10.1016/j.physb.2011.06.048
42. Hoffmann, K.-H., Botkin, N.D.: Multiphase flows with phase transitions: Models
and numerics. JP J. Heat Mass Transf. 6(2), 73–86 (2012)
43. Kovtanyuk, A.E., Botkin, N.D., Hoffmann, K.-H.: Numerical simulations
of a coupled radiative-conductive heat transfer model using a modified
Monte Carlo method. Int. J. Heat Mass Transf. 55(4), 649–654 (2012).
https://doi.org/10.1016/j.ijheatmasstransfer.2011.10.045
44. Amler, T.G., Botkin, N.D., Hoffmann, K.-H., Ruf, K.A.: Regularity of solu-
tions of a phase field model. Dyn. Partial Differ. Equ. 10(4), 353–365 (2013).
https://doi.org/10.4310/DPDE.2013.v10.n4.a3
45. Botkin, N.D., Hoffmann, K.-H., Marx, D., Starovoitov, V.N., Turova, V.L.: Mod-
eling in the development of an elasto-optical biosensor based on nanostructures.
International Journal of Biomathematics and Biostatistics 2(2), 191–202 (2013)
46. Botkin, N., Turova, V.: Numerical construction of viable sets for au-
tonomous conflict control systems. Mathematics 2(2), 68–82 (2014).
https://doi.org/10.3390/math2020068
47. Kovtanyuk, A.E., Chebotarev, A.Yu., Botkin, N.D., Hoffmann, K.-H.: Solvability
of P1 approximation of a conductive-radiative heat transfer problem. Appl.
Math. Comput. 249, 247–252 (2014). https://doi.org/10.1016/j.amc.2014.10.054
48. Kovtanyuk, A.E., Chebotarev, A.Y., Botkin, N.D., Hoffmann, K.-H.: The-
oretical analysis of an optimal control problem of conductive-convective-
radiative heat transfer. J. Math. Anal. Appl. 412(1), 520–528 (2014).
https://doi.org/10.1016/j.jmaa.2013.11.003
49. Kovtanyuk, A.E., Chebotarev, A.Y., Botkin, N.D., Hoffmann, K.-H.: The unique
solvability of a complex 3D heat transfer problem. J. Math. Anal. Appl. 409(2),
808–815 (2014). https://doi.org/10.1016/j.jmaa.2013.07.054
50. Lampe, R., Botkin, N., Turova, V., Blumenstein, T., Alves-Pinto, A.:
(2014) Mathematical modelling of cerebral blood circulation and cerebral
autoregulation: Towards preventing intracranial hemorrhages in preterm
newborns. Comput. Math. Methods Med. 2014 art. no. 965275 (2014).
https://doi.org/10.1155/2014/965275
51. Botkin, N.D., Turova, V.L.: Examples of computed viability kernels. Trudy Inst.
Mat. i Mekh. UrO RAN 21(2), 306–319 (2015)
52. Fraçkowiak, A., Botkin, N.D., Cialkowski, M., Hoffmann, K.-H.: Iterative
algorithm for solving the inverse heat conduction problems with the un-
known source function. Inverse Probl. Sci. Eng. 23(6), 1056–1071 (2015).
https://doi.org/10.1080/17415977.2014.986723
53. Kovtanyuk, A.E., Chebotarev, A.Y., Botkin, N.D., Hoffmann, K.-H.:
Unique solvability of a steady-state complex heat transfer model.
Commun. Nonlinear Sci. Numer. Simul. 20(3), 776–784 (2015).
https://doi.org/10.1016/j.cnsns.2014.06.040
The Scientific Contribution of Nikolai D. Botkin ix
54. Lampe, R., Botkin, N., Turova, V., Blumenstein, T., Alves-Pinto, A.: Math-
ematical modeling of cerebral oxygenation in premature infants. Eur. J.
Paediatr. Neurol. 19(Suppl. 1), S54–S55 (2015). https://doi.org/10.1016/S1090-
3798(15)30179-3
55. Botkin, N.D., Brokate, M., El Behi-Gornostaeva, E.G.: One-phase flow in
porous media with hysteresis. Physica B Condens. Matter 486, 183–186 (2016).
https://doi.org/10.1016/j.physb.2015.08.039
56. Chebotarev, A.Yu., Kovtanyuk, A.E., Grenkin, G.V., Botkin, N.D.,
Hoffmann, K.-H.: Nondegeneracy of optimality conditions in control prob-
lems for a radiative-conductive heat transfer model. Appl. Math. Comput. 289,
371–380 (2016). https://doi.org/10.1016/j.amc.2016.05.036
57. Grenkin, G.V., Chebotarev, A.Y., Kovtanyuk, A.E., Botkin, N.D.,
Hoffmann, K.-H.: Boundary optimal control problem of complex heat
transfer model. J. Math. Anal. Appl. 433 (2), 1243–1260 (2016).
https://doi.org/10.1016/j.jmaa.2015.08.049
58. Kovtanyuk, A.E., Chebotarev, A.Y., Botkin, N.D., Hoffmann, K.-H.: Op-
timal boundary control of a steady-state heat transfer model account-
ing for radiative effects. J. Math. Anal. Appl. 439(2), 678–689 (2016).
https://doi.org/10.1016/j.jmaa.2016.03.016
59. Botkin, N., Turova, V., Diepolder, J., Bittner, M., Holzapfel, F.: Aircraft control
during cruise flight in windshear conditions: Viability approach. Dyn. Games
Appl. 7(4), 594–608 (2017). https://doi.org/10.1007/s13235-017-0215-9
60. Botkin, N.D., Kovtanyuk, A.E., Turova, V.L., Sidorenko, I.N.,
Lampe, R.: Direct modeling of blood flow through the vascular net-
work of the germinal matrix. Comput. Biol. Med. 92, 147–155 (2018).
https://doi.org/10.1016/j.compbiomed.2017.11.010
61. Botkin, N., Turova, V., Diepolder, J., Holzapfel, F.: Computation of viability
kernels on grid computers for aircraft control in windshear. Adv. Sci. Technol.
Eng. Syst. J. 3(1), 502–510 (2018). https://doi.org/10.25046/aj030161
62. Chebotarev, A.Y., Grenkin, G.V., Kovtanyuk, A.E., Botkin, N.D.,
Hoffmann, K.-H.: Diffusion approximation of the radiative-conductive heat
transfer model with Fresnel matching conditions. Commun. Nonlinear Sci.
Numer. Simul. 57, 290–298 (2018). https://doi.org/10.1016/j.cnsns.2017.10.004
63. Chebotarev, A.Y., Grenkin, G.V., Kovtanyuk, A.E., Botkin, N.D.,
Hoffmann, K.-H.: Inverse problem with finite overdetermination for steady-
state equations of radiative heat exchange. J. Math. Anal. Appl. 460(2), 737–744
(2018). https://doi.org/10.1016/j.jmaa.2017.12.015
64. Sidorenko, I., Turova, V., Botkin, N., Eckardt, L., Alves-Pinto, A.,
Felderhoff-Müser, U., Rieger-Fackeldey, E., Lampe, R.: Modeling cerebral
blood flow dependence on carbon dioxide and mean arterial blood pressure in
the immature brain with accounting for the germinal matrix. Front. Neurol. 9,
812 (2018). https://doi.org/10.3389/fneur.2018.00812
65. Botkin, N.D., Kovtanyuk, A.E, Turova, V.L., Sidorenko, I.N., Lampe, R.:
Accounting for tube hematocrit in modeling of blood flow in cerebral capillary
networks. Comput. Math. Methods Med. 2019, Article ID 4235937 (2019).
https://doi.org/10.1155/2019/4235937
x
66. Botkin, N., Martynov, K., Turova, V., Diepolder, J.: Generation of dangerous
disturbances for flight systems. Dyn. Games Appl. 9(3), 628–651 (2019).
https://doi.org/10.1007/s13235-018-0259-5
67. Botkin, N.D., Turova, V.L., Kovtanyuk, A.E., Sidorenko, I.N., Lampe, R.:
Extended model of impaired cerebral autoregulation in preterm infants:
Heuristic feedback control. Math. Biosci. Eng. 16(4), 2334–2352 (2019).
https://doi.org/10.3934/mbe.2019117
68. Chebotarev, A.Y., Kovtanyuk, A.E., Botkin, N.D.: Problem of radiation heat
exchange with boundary conditions of the Cauchy type. Commun. Nonlinear Sci.
Numer. Simul. 75, 262–269 (2019). https://doi.org/10.1016/j.cnsns.2019.01.028
69. Kovtanyuk, A.E., Chebotarev, A.Y., Botkin, N.D., Turova, V.L., Sidorenko, I.N.,
Lampe, R.: Continuum model of oxygen transport in brain. J. Math. Anal. Appl.
474(2), 1352–1363 (2019). https://doi.org/10.1016/j.jmaa.2019.02.020
70. Lampe, R., Turova, V., Botkin, N., Eckardt, L., Felderhoff-Müser, U.,
Rieger-Fackeldey, E., Alves-Pinto, A., Kovtanyuk, A., Sidorenko, I.: Post-
natal paraclinical parameters associated to occurrence of intracerebral
hemorrhage in preterm infants. Neuropediatrics 50(2), 103–110 (2019).
https://doi.org/10.1055/s-0038-1677515
71. Kovtanyuk, A.E., Chebotarev, A.Y., Botkin, N.D., Turova, V.L., Sidorenko, I.N.,
Lampe, R.: Nonstationary model of oxygen transport in brain tis-
sue. Comput. Math. Methods Med. 2020, Article ID 4861654 (2020).
https://doi.org/10.1155/2020/4861654
72. Lampe, R., Rieger-Fackeldey, E., Sidorenko, I., Turova, V., Botkin, N.,
Eckardt, L., Alves-Pinto, A., Kovtanyuk, A., Schündeln, M., Felderhoff-Müser, U.:
Assessing key clinical parameters before and after intraventricular hem-
orrhage in very preterm infants. Eur. J. Paediatr. 2019, 1–9 (2020).
https://doi.org/10.1007/s00431-020-03585-9
73. Sidorenko, I., Turova, V., Botkin, N., Kovtanyuk, A., Eckardt, L., Alves-Pinto, A.,
Felderhoff-Müser, U., Rieger-Fackeldey, E., Lampe, R.: Assessing haemorrhage-
critical values of cerebral blood flow by modelling biomechanical stresses on
capillaries in the immature brain. Sci. Rep. 10(1), Article ID 14196 (2020).
https://doi.org/10.1038/s41598-020-71087-7
74. Botkin, N., Turova, V., Hosseini, B., Diepolder, J., Holzapfel, F.: Tracking
aircraft trajectories in the presence of wind disturbances. Math. Control Relat.
Fields (accepted)
75. Kovtanyuk, A.E., Chebotarev, A.Yu, Botkin, N.D., Turova, V.L., Sidorenko, I.N.,
Lampe, R.: Modeling the pressure distribution in a spatially averaged cerebral
capillary network. Math. Control Relat. Fields (accepted)
Papers and Chapters in Peer-Reviewed Collections, Books or
Book Series
76. Botkin, N.D.: Numerical construction of sections of the positional absorption set
in a linear differential game. In: Subbotin, A.I., Patsko, V.S. (eds.) Algorithms
and Programs for Solution of Linear Differential Games (Materials on Computer
Software) [in Russian], pp. 5–38. IMM UNTs Akad Nauk SSSR, Sverdlovsk (1984)
The Scientific Contribution of Nikolai D. Botkin xi
77. Botkin, N.D., Zarkh, M.A.: Error estimate for the construction of the positional
absorption set in a linear differential game. In: Subbotin, A.I., Patsko, V.S. (eds.)
Algorithms and Programs for Solving Linear Differential Games (Materials on
Computer Software) [in Russian], pp. 39–80. IMM UNTs Akad Nauk SSSR,
Sverdlovsk (1984)
78. Botkin, N.D., Kein, V.M., Patsko, V.S.: Solution to an aircraft landing problem
in a minimax statement. In: Malyshev, V.V. et al. (eds.) Collection of Scientific
Works: Optimization of Control of Aircraft and Their Systems [in Russian],
pp. 8–15. MAI, Moscow (1988)
79. Botkin, N.D., Krasov, A.I.: Positional control in a model problem of aircraft
runway acceleration. In: Subbotin, A.I., Tarasjev, A.M. (eds.) Positional Control
with a Guaranteed Result (Collection of scientific works) [in Russian], pp. 22–32.
IMM UrO Akad. Nauk SSSR, Sverdlovsk (1988)
80. Botkin, N.D, Kein, V.M., Patsko, V.S.: Application of differential game the-
ory methods to an aircraft control problem on landing. In: Subbotin, A.I.,
Tarasjev, A.M. (eds.) Collection of Scientific Works: Positional Control with
a Guaranteed Result [in Russian], pp. 33–44. IMM UrO Akad. Nauk SSSR,
Sverdlovsk (1988)
81. Botkin, N.D., Zhukov, S.P., Krasov, A.I.: Combined method of aircraft control
on landing. In: Subbotin, A.I., Ushakov, V.N. (eds.) Collection of Scientific
Works: Control in Dynamical Systems [in Russian], pp. 18–30. IMM UrO Akad.
Nauk SSSR, Sverdlovsk (1990)
82. Botkin, N.D., Zarkh, M.A., Patsko, V.S.: Numerical solution of linear differential
games. In: Hämäläinen, R.P., Ehtamo, H.K. (eds.) Lecture Notes in Control
and Information Sciences, vol. 156: Differential Games – Developments in
Modelling and Computation, pp. 226–234. Springer, Berlin, Heidelberg (1991).
https://doi.org/10.1007/BFb0040243
83. Botkin, N.D., Kein, V.M., Patsko, V.S., Turova, V.L., Zarkh, M.A.: Numerical
methods for solving differential games, prospective applications to technical
problems. In: Bulirsch, R., Kraft, D. (eds.) ISNM International Series of Nu-
merical Mathematics, vol. 115: Computational Optimal Control, pp. 137–145.
Birkhäuser, Basel (1994). https://doi.org/10.1007/978-3-0348-8497-6 12
84. Botkin, N.D., Turova-Botkina, V.L.: An algorithm for finding the Cheby-
shev center of a convex polyhedron. In: Henry, J., Yon, J.P. (eds.) Lecture
Notes in Control and Information Sciences, vol. 197: Proceedings of the 16th
IFIP-TC7 Conference on System Modelling and Optimization, Compiègne,
France, July 5–9, 1993., pp. 833–844. Springer, Berlin, Heidelberg (1994).
https://doi.org/10.1007/BFb0035533
85. Hoffmann, K.-H., Botkin, N.D.: Homogenization of a model describing vibra-
tion of nonlinear thin plates excited by piezopatches. In: Hoffmann, K.-H.,
Leugering, G., Trolzsch, F. (eds.) ISNM International Series of Numerical Math-
ematics, vol. 133: Optimal Control of Partial Differential Equations, pp. 191–200.
Birkhäuser, Basel (1999). https://doi.org/10.1007/978-3-0348-8691-8 16
86. Botkin, N.D., Hoffmann, K.-H.: Fully coupled model of a nonlinear thin plate ex-
cited by piezoelectric actuators. In: Hoffmann, K.-H., Lasiecka, I., Leugering, G.,
Sprekels, J., Tröltzsch, F. (eds.) ISNM International Series of Numerical
Mathematics, vol. 139: Optimal Control of Complex Structures, pp. 107–118.
xii
Birkhäuser, Basel (2001). https://doi.org/10.1007/978-3-0348-8148-7 9
87. Hoffmann, K.-H., Botkin, N.D.: Real-time optimization and stabilization of
distributed parameter systems with piezoelectric elements. In: Grötschel, M.,
Krumke, S.O., Rambau, J. (eds.) Online Optimization of Large Scale Systems,
pp. 205–228. Springer, Berlin, Heidelberg (2001). https://doi.org/10.1007/978-3-
662-04331-8 14
88. Botkin, N.D., Hoffmann, K.-H., Turova, V.L.: Freezing of living cells: Mathemat-
ical models and design of optimal cooling protocols. In: Leugering, G., Engell, S.,
Griewank, A., Hinze, M., Rannacher, R., Schulz, V., Ulbrich, M., Ulbrich, S.
(eds.) ISNM International Series of Numerical Mathematics, vol. 160: Con-
strained Optimization and Optimal Control for Partial Differential Equations,
pp. 521–540. Birkhäuser, Basel (2012). https://doi.org/10.1007/978-3-0348-0133-
1 27
89. Botkin, N., Hoffmann, K.-H., Mayer, N., Turova, V.: Computation of value
functions in nonlinear differential games with state constraints. In: Hömberg, D.,
Tröltzsch, F. (eds.) IFIP Advances in Information and Communication Tech-
nology, vol. 391: Proceedings of IFIP Conference on System Modeling and
Optimization (CSMO 2011), pp. 235–244. Springer, Berlin, Heidelberg (2013).
https://doi.org/10.1007/978-3-642-36062-6 24
90. Botkin, N.D., Hoffmann, K.-H., Turova, V.L.: Mathematical modeling and
simulations in cryopreservation of living cells. In: Colvert, A., Coty, H. (eds.)
Cryopreservation: Technologies, Applications and Risks/Outcomes, pp. 109–176.
Nova Science Publishers Inc. (2013)
91. Botkin, N.D, Turova, V.L.: Dynamic programming approach to aircraft control
in a windshear. In: Kr̆ivan, V., Zaccour, G. (eds.) Annals of the International
Society of Dynamic Games, vol. 13: Advances in Dynamic Games: Theory,
Applications, and Numerical Methods, pp. 53–69. Birkhäuser, Cham (2013).
https://doi.org/10.1007/978-3-319-02690-9 3
92. Botkin, N., Turova, V.: Simulation of acoustic wave propagation in anisotropic
media using dynamic programming technique. In: Pötzsche, C., Heuberger, C.,
Kaltenbacher, B., Rendl, F. (eds.) IFIP Advances in Information and Communi-
cation Technology, vol. 443: Proceedings of IFIP Conference on System Modeling
and Optimization (CSMO 2013), pp. 36–51. Springer, Berlin, Heidelberg (2014).
https://doi.org/10.1007/978-3-662-45504-3 5
93. Hoffmann, K.-H., Botkin, N.D., Turova, V.L.: Models and optimal control in
freezing and thawing of living cells and tissues. In: Leugering, G., Benner, P.,
Engell, S., Griewank, A., Harbrecht, H., Hinze, M., Rannacher, R., Ulbrich, S.
(eds.) ISNM International Series of Numerical Mathematics, vol. 165: Trends
in PDE Constrained Optimization, pp. 155–172. Birkhäuser, Cham (2014).
https://doi.org/10.1007/978-3-319-05083-6 10
94. Botkin, N., Turova, V.: Aircraft runway acceleration in the presence of severe
wind gusts. In: Bociu, L., Désidéri, J.A., Habbal, A. (eds.) Advances in Informa-
tion and Communication Technology, vol. 494: Proceedings of IFIP Conference
on System Modeling and Optimization (CSMO 2015), pp. 147–158. Springer,
Cham (2016). https://doi.org/10.1007/978-3-319-55795-3 13
95. Botkin, N., Turova, V.: Optimal abort landing in the presence of severe winds-
hears. In: Bociu, L., Désidéri, J.A., Habbal, A. (eds) Advances in Information
The Scientific Contribution of Nikolai D. Botkin xiii
and Communication Technology, vol. 494: Proceedings of IFIP Conference on
System Modeling and Optimization (CSMO 2015), pp. 137–146. Springer, Cham
(2016). https://doi.org/10.1007/978-3-319-55795-3 12
96. Chebotarev, A.Y., Kovtanyuk, A.E., Botkin, N.D., Hoffmann, K.-H.: Strong
optimal controls in a steady-state problem of complex heat transfer. In:
Bociu, L., Désidéri, J.A., Habbal, A. (eds.) IFIP Advances in Information and
Communication Technology, vol. 494: Proceedings of IFIP Conference on System
Modeling and Optimization (CSMO 2015), pp. 209–219. Springer, Cham (2016).
https://doi.org/10.1007/978-3-319-55795-3 19
97. Botkin, N., Diepolder, J., Turova, V., Bittner, M., Holzapfel, F.: Viability ap-
proach to aircraft control in wind shear conditions. In: Apaloo, J., Viscolani, B.
(eds.) Annals of the International Society of Dynamic Games, vol. 15: Advances
in Dynamic and Mean Field Games: Theory, Applications, and Numerical
Methods, pp. 325–343. Birkhäuser, Cham (2017). https://doi.org/10.1007/978-
3-319-70619-1 15
98. Turova, V., Botkin, N., Alves-Pinto, A., Blumenstein, T., Rieger-Fackeldey, E.,
Lampe, R.: Modeling autoregulation of cerebral blood flow using viability
approach. In: Apaloo, J., Viscolani, B. (eds.) Annals of the International Society
of Dynamic Games, vol. 15: Advances in Dynamic and Mean Field Games:
Theory, Applications, and Numerical Methods, pp. 345–363. Birkhäuser, Cham
(2017). https://doi.org/10.1007/978-3-319-70619-1 16
99. Botkin, N.D., Diepolder, J., Turova, V.L.: Viability approach to simulation
of an adaptive controller. In: Kalise, D., Kunish, K., Rao, Z. (eds.) Radon
Series on Computational and Applied Mathematics, Vol. 21: Hamilton-
Jacobi-Bellman Equations: Numerical Methods and Applications in Optimal
Control, pp. 43–60. De Gruyter GmbH, Berlin, Munich, Boston (2018).
https://doi.org/10.1515/9783110543599-003
100. Botkin, N.D., Golubev, A.E., Turova, V.L.: Aircraft guiding in windshear
through differential game-based overload control. In: Jadachowski, L. (ed.) IFAC
Proceedings Volume, vol. 52(16): 11th IFAC Symposium on Nonlinear Control
Systems NOLCOS 2019, Vienna, Austria, September 4-6, 2019, pp. 706–711.
IFAC-PapersOnLine (2019). https://doi.org/10.1016/j.ifacol.2019.12.045
101. Diepolder, J., Botkin, N., Holzapfel, F.: Optimal disturbance generation for
flight control law testing. In: Jadachowski, L. (ed.) IFAC Proceedings Volume,
vol. 52(16): 11th IFAC Symposium on Nonlinear Control Systems NOLCOS
2019, Vienna, Austria, September 4-6, 2019, pp. 730–734. IFAC-PapersOnLine
(2019). https://doi.org/10.1016/j.ifacol.2019.12.049
102. Golubev, A.E., Botkin, N.D., Krishchenko, A.P.: Backstepping control of aircraft
take-off in windshear. In: Jadachowski, L. (ed.) IFAC Proceedings Volume,
vol. 52(16): 11th IFAC Symposium on Nonlinear Control Systems NOLCOS
2019, Vienna, Austria, September 4-6, 2019, pp. 712–717. IFAC-PapersOnLine
(2019). https://doi.org/10.1016/j.ifacol.2019.12.046
103. Martynov, K., Botkin, N.D., Turova, V.L., Diepolder, J.: Quick construction
of dangerous disturbances in conflict control problems. In: Ramsey, D.M.,
Renault, J. (eds.) Annals of the International Society of Dynamic Games, vol. 17:
Advances in Dynamic Games: Games of Conflict, Evolutionary Games, Economic
Games, and Games Involving Common Interest, pp. 3–24. Birkhäuser, Cham
(2020). https://doi.org/10.1007/978-3-030-56534-3
xiv
Patents
104. Botkin, N.D., Kein, V.M., Krasov, A.I., Patsko, V. S.: Device for aircraft control
during the landing approach. Author certificate N1450250. Declared by Academy
of Civil Aviation (Leningrad). Request N4141626; registered 8.09.88 (1988)
105. Botkin, N., Degistrici, Ö., Fassbender, B., Simonsmeier, J., Thie, M.: Zahn-
Einfrierer-Behälter. Deutches Patent- und Markenamt. DE 10 2005 047 438 A1,
2007.04.05 (8) (2007)
Papers in Conference Proceedings
106. Botkin, N.D., Patsko, V.S.: Numerical solution of linear differential game. In:
Dimovski, I., Stoyanov, J. (eds.) Proceedings of the Third Conference “Differ-
ential equations and applications” I. Rousse, Bulgaria, June 30–July 6, 1985 [in
Russian], pp. 543–546. ‘Angel Kancev’ Tech. Univ., Rousse (1987)
107. Botkin, N.D., Patsko, V.S., Turova, V.L., Zarkh, M.A., Kein, V.M.: Aircraft
control problems in the presence of windshear. In: Preprint Volume of the
Fifth International Symposium on Dynamic Games and Applications. Grimentz,
Switzerland, July 15–17, 1992, pp. 133–148. Université de Genève (1992)
108. Botkin, N.: Identification of parameters for thermoelasticity models. In:
Kleinschmidt, P., Bachem, A., Derigs, U., Fischer, D., Leopold-Wildburger, U.,
Mohring, R. (eds.) Operations Research Proceedings 1995, pp. 173–177. Springer,
Berlin, Heidelberg (1996). https://doi.org/10.1007/978-3-642-80117-4 30
109. Botkin, N.D.: Identification of unknown parameters for heat conductivity
equations. In: Carlomagno, G.M., Brebbia, C.A. (eds.) Proceedings of the VII
International Conference on Computational Methods and Experimental Mea-
surements (CMEM95). Capri, Italy, May 16–18, 1995. Computational Mechanics
Publications, pp. 101–108 (1995)
110. Botkin, N.D.: Identification of parameters for heat conductivity equations.
In: Gottlieb, J., DuChateau, P. (eds.) Parameter Identification and Inverse
Problems in Hydrology, Geology and Ecology, vol. 23: Proceedings of a workshop
held in Karlsruhe, Germany, April 10–12, 1995, pp. 133–142. Water Science
and Technology Library, Kluwer Academic Publishers, Dordrecht (1996).
https://doi.org/10.1007/978-94-009-1704-0 7
111. Botkin, N.: Parameters estimation of some electro-elasticity models. In:
Bainov, D. (ed.) Proceedings of the Seventh International Colloquium on
Differential Equations. Plovdiv, Bulgaria, 18–23 August, 1996, pp. 31–38. VSP,
Utrecht, the Netherlands (1997)
112. Botkin, N.D.: Differentiability of solutions of an electro-elasticity model w.r.t.
parameters. In: Bainov, D. (ed.) Proceedings of the Eighth International
Colloquium on Differential Equations. Plovdiv, Bulgaria, 18–23 August, 1997,
pp. 89–96. VSP, Utrecht, the Netherlands (1998)
113. Botkin, N.D., Hoffmann, K.-H.: A fully coupled model of a nonlinear thin plate.
In: Hoffmann, K.-H. (ed.) Proceedings of the 1st caesarium. Bonn, November
17–19, 1999. Smart materials, pp. 9–22. Springer, Berlin, Heidelberg (2001).
https://doi.org/10.1007/978-3-642-56855-8 2
The Scientific Contribution of Nikolai D. Botkin xv
114. Botkin, N.D., Schlensog, M., Tewes, M., Turova, V.L.: A mathematical model of
a biosensor. In: Laudon, M., Romanowicz, B.F. (eds.) Technical Proceedings of
the 2001 International Conference on Modeling and Simulation of Microsystems:
MSM 2001. Hilton Head Island, SC, USA, March 19–21, 2001. 2001 ACRS Joint
Meeting (MSM/ICCN), pp. 231–234. Computational Publications, University of
Michigan (2001)
115. Winzek, B., Sterzl, T., Rumpf, H., Botkin, N., Quandt, E.: Thin film shape
memory composites. In: NATO Conference on Martensitic Phase Transformation.
Metz, France, April 23–26, 2002, pp. 1–15 (2002)
116. Botkin, N.D., Hoffmann, K.-H., Starovoitov, V.N, Turova, V.L.: Modeling the
interaction between bristle elastic structures and fluids. In: Technical Proceedings
of the 2003 Nanotechnology Conference and Trade Show, vol. 1: Proceedings of
the 6th International Conference on Modeling and Simulation of Microsystems
(MSM). San Francisco, USA, February 23–27, 2003, pp. 126–129 (2003)
117. Botkin, N.D., Hoffmann, K.-H., Starovoitov, V.N., Turova, V.L.: Treatment
of the interface between fine elastic structures and fluids. In: Fradkov, A.L.,
Churilov, A.N. (eds.) 2003 IEEE International Workshop on Workload Char-
acterization (IEEE Cat. No.03EX775), vol. 4: Proceedings of the International
Conference “Physics and Control”. St. Petersburg, Russia, August 20–22,
2003, pp. 1367–1372. IEEE, St. Petersburg, Russia (2003). https://doi.org/
10.1109/PHYCON.2003.1237107
118. Botkin, N.D., Hoffmann, K.-H., Pykhteev, O.A., Turova, V.L.: Numerical
computation of dispersion relations for multi-layered anisotropic structures.
In: Technical Proceedings of the 2004 Nanotechnology Conference and Trade
Show, vol. 2: Proceedings of the 7th International Conference on Modeling and
Simulation of Microsystems (MSM). Boston, Massachusetts, USA, March 9–11,
2004, pp. 411–414 (2004)
119. Botkin, N.D., Hoffmann, K.-H., Pykhteev, O.A., Turova, V.L.: Dispersion
relations for acoustic waves in heterogeneous multi-layered structures contacting
with fluids. In: Proceedings of the First International Conference on Modeling,
Simulation and Applied Optimization (ICMSAO ’05). Sharjah, U.A.E., February
1–3, 2005. American University of Sharjah (2005)
120. Hassdorf, R., Feydt, J., Thienhaus, S., Buforn, L., Conté, N., Pykhteev, O.,
Kruz̆ik, M., Botkin, N., Moske, M.: Spherical load indentation in submi-
cron NiTiCu shape memory thin films. In: Bahr, D.F., Cheng, Y.T., Huber, N.,
Mann, A.B., Wah, K.J. (eds.) MRS Online Proceedings Library Archive, vol. 841:
Proceedings of the 2004 Material Research Society Fall Meeting, Symposium R -
Fundamentals of Nanoindentation and Nanotribology III. Boston, MA, November
29–December 3, 2004, pp. R9.7.1–R9.7.6. Cambridge University Press (2005).
This paper is a Ribbon Award winner. https://doi.org/10.1557/PROC-841-R9.7
121. Melikyan, A., Botkin, N., Turova, V.: Modelling of propagation in anisotropic
media using differential game methods. In: Zı́tek, P. (ed.) IFAC Proceedings Vol-
umes, vol. 38(1): 16th IFAC World Congress. Prague, July 3–8, 2005, pp. 584–589.
IFAC-PapersOnline (2005). https://doi.org/10.3182/20050703-6-CZ-1902.00098
122. Melikyan, A.A., Botkin, N.D., Turova, V.L.: Singularity phenomena in ray
propagation in anisotropic media. In: Fradkov, A.L., Churilov, A.N. (eds.) Pro-
ceedings of the 2005 International Conference on Physics and Control (PhysCon
2005). St. Petersburg, Russia, August 24–26, 2005, pp. 373–378. IEEE (2005).
xvi
https://doi.org/10.1109/PHYCON.2005.1514010
123. Botkin, N.D., Pykhteev, O.A., Starovoitova, B.N., Turova, V.L., Hoffmann, K.-H.:
Two complementary approaches to modelling a biosensor. In: Hamza, M.H.
(ed.) Proceedings of the 15th IASTED International Conference on Applied
Simulation and Modelling 2006. Rhodos, Greece, June 26–28, 2006, pp. 525–530.
ACTA Press (2006)
124. Hassdorf, R., Feydt, J., Thienhaus, S., Buforn, L., Conté, N., Pykhteev, O.,
Kruz̆ik, M., Botkin, N., Moske, M.: Probing superelasticity in NiTi-based shape
memory thin films and foils. In: Mertmann, M. (ed.) SMST-2004: Proceedings of
the International Conference on Shape Memory and Superelastic Technologies.
Baden-Baden, Germany, October 3–7, 2004, pp. 399–407. ASM International
Materials Park, Ohio 44073-0002 (2006)
125. Alkadhi, R.M., Botkin, N.D., Hoffmann, K.-H.: Application of a dynamic
programming method to enlarged version of Stoleru’s economic model. In:
IFAC Proceedings Volumes, vol. 45(25): 15th IFAC Workshop on Control
Applications of Optimization. Rimini, Italy, September 13–16, 2012, pp. 14–20.
IFAC-PapersOnline (2012). https://doi.org/10.3182/20120913-4-IT-4027.00005
126. Botkin, N.D., Brokate, M., Hoffmann, K.-H., Pykhteev, O.A., Turova, V.L.:
Simulation of hysteretic effects in multi-phase flows in aquifers. In: AIP
Conference Proceedings, vol. 1479(1), art. no. 1243, pp. 1243–1246 (2012).
https://doi.org/10.1063/1.4756378
127. Botkin, N.D., Turova, V.L.: Application of dynamic programming approach to
aircraft take-off in a windshear. In: AIP Conference Proceedings, vol. 1479(1),
art. no. 1226, pp. 1226–1229 (2012). https://doi.org/10.1063/1.4756373
128. Botkin, N., Turova, V.: Preface of the “Modeling of multiphase flows in porous
and fissured media”. In: AIP Conference Proceedings, vol. 1479(1), art. no. 1238,
pp. 1238 (2012). https://doi.org/10.1063/1.4756376
129. Botkin, N., Turova, V.: Preface of the “Session on Hamilton-Jacobi equations
arising from optimal control problems and differential games: Analysis, numerical
methods and applications”. In: AIP Conference Proceedings, vol. 1479(1),
art. no. 1220, pp. 1220–1221 (2012). https://doi.org/10.1063/1.4756371
130. Botkin, N., Turova, V., Lampe, R.: Feedback control of impaired cerebral
autoregulation in preterm infants: Mathematical modelling. In: 2017 25th
Mediterranean Conference on Control and Automation (MED 2017). Val-
letta, Malta, July 3–6, 2017, art. no. 7984123, pp. 229–234. IEEE (2017).
https://doi.org/10.1109/MED.2017.7984123
131. Chebotarev, A.Y., Kovtanyuk, A.E., Botkin, N.D.: Optimal boundary
temperature control in the model of radiative heat transfer. In: AIP
Conference Proceedings, vol. 1907(1), art. no. 030044, pp. 1–6 (2017).
https://doi.org/10.1063/1.5012666
132. Kovtanyuk, A.E., Chebotarev, A.Y., Grenkin, G.V., Botkin, N.D.,
Hoffmann, K.-H.: Analysis of thermal processes in a multilayer biotissue
exposed to optical radiation. In: Proceedings of the International Conference
Days on Diffraction 2017 (DD 2017). St. Petersburg, Russia, June 19–23, 2017,
pp. 194–199 (2017). https://doi.org/10.1109/DD.2017.8168022
133. Martynov, K., Botkin, N., Turova, V., Diepolder, J.: Real-time control of
aircraft take-off in windshear. Part I: Aircraft model and control schemes. In:
The Scientific Contribution of Nikolai D. Botkin xvii
2017 25th Mediterranean Conference on Control and Automation (MED 2017).
Valletta, Malta, July 3–6, 2017, art. no. 7984131, pp. 277–284. IEEE (2017).
https://doi.org/10.1109/MED.2017.7984131
134. Martynov, K., Botkin, N., Turova, V., Diepolder, J.: Real-time control of aircraft
take-off in windshear. Part II: Simulations and model enhancement. In: 2017
25th Mediterranean Conference on Control and Automation (MED 2017).
Valletta, Malta, July 3–6, 2017, art. no. 7984132, pp. 285–290. IEEE (2017).
https://doi.org/10.1109/MED.2017.7984132
135. Diepolder, J., Piprek, P., Botkin, N., Turova, V., Holzapfel, F.: A robust
aircraft control approach in the presence of wind using viability theory. In:
2017 Australian and New Zealand Control Conference (ANZCC 2017). Gold
Coast, QLD, Australia, December 17–20, 2017, pp. 155–160. IEEE (2018).
https://doi.org/10.1109/ANZCC.2017.8298503
136. Kovtanyuk, A.E., Chebotarev, A.Yu., Dekalchuk, A.A., Botkin, N.D., Lampe, R.:
Analysis of a mathematical model of oxygen transport in brain. In: Proceedings of
the International Conference Days on Diffraction (DD 2018). St. Petersburg, June
4–8, 2018, pp. 187–191. IEEE (2018). https://doi.org/10.1109/DD.2018.8553338
137. Kovtanyuk, A.E., Chebotarev, A.Yu., Dekalchuk, A.A., Botkin, N.D., Lampe, R.:
An iterative algorithm for solving an initial boundary value problem of oxygen
transport in brain. In: Proceedings of the International Conference Days on
Diffraction 2019 (DD 2019). St. Petersburg, June 3–7, 2019, pp. 99–104. IEEE
(2019). https://doi.org/10.1109/DD46733.2019.9016443
138. Hosseini, S., Botkin, N., Diepolder, J., Holzapfel, F.: Robust optimal input design
for flight vehicle system identification. In: AIAA Scitech 2020 Forum, Orlando,
FL, January 6–10, 2020, p. 0290 (2020). https://doi.org/10.2514/6.2020-0290
Preprints and Scientific Reports
139. Botkin, N.D.: Approximation error in a differential game. Dep. v VINITI
11.04.83, No. 1910-83 DEP, pp. 1–31 (1983) [in Russian]
140. Botkin, N.D., Kein, V.M., Krasov, A.I., Patsko, V.S.: Research on the improve-
ment of on-board and ground-based aircraft control systems. Control of the
aircraft lateral motion on landing under wind disturbance conditions. Report
81104592/02830078880 (All-Union Scientific and Technical Information Center -
VNTIZ), L. - Sverdlovsk, pp. 1–78 (1983) [in Russian]
141. Botkin, N.D.: Error estimation of numerical constructions in a quasi-linear
differential game. Dep. v VINITI 26.05.86, No. 3779-B, pp. 1–27 (1986) [in
Russian]
142. Botkin, N.D., Patsko, V.S.: Development of numerical methods for constructing
extreme wind disturbances acting on an aircraft at the landing stage. Analysis
of the application of the differential game theory methods for simulating
wind disturbances. Report 01880003467/02880044271 (All-Union Scientific and
Technical Information Center – VNTIZ), Sverdlovsk, pp. 1–46 (1987) [in Russian]
143. Botkin, N.D., Patsko, V.S., Turova, V.L.: Development of numerical methods
for constructing extreme wind disturbances acting on an aircraft at the landing
stage. Development of algorithms for constructing extreme wind disturbances.
Report 01880003467/02880054701 (All-Union Scientific and Technical Informa-
tion Center – VNTIZ), Sverdlovsk, pp. 1–58 (1987) [in Russian]
xviii
144. Botkin, N.D., Turova, V. L.: Development of numerical methods for constructing
extreme wind disturbances acting on an aircraft at the landing stage. Development
of a package of applied programs for the synthesis of extreme wind disturbances
at the landing stage. Report 01880003467/02880069889 (All-Union Scientific and
Technical Information Center – VNTIZ), Sverdlovsk, pp. 1–39 (1988) [in Russian]
145. Botkin, N.D., Turova, V.L., Ivanov, A.G.: Development of numerical methods
for constructing extreme wind disturbances acting on an aircraft at the landing
stage. Recommendations for simulating extreme wind disturbances. Report
01880003467/02880045178 (All-Union Scientific and Technical Information
Center – VNTIZ), Sverdlovsk, pp. 1–51 (1988) [in Russian]
146. Botkin, N. D., Patsko, V. S., Zarkh, M. A.: Numerical solution of linear differ-
ential games. IV Intern. Symposium on Differential Games and Applications.
Helsinki, August 9–10, 1990. Preprint (1990)
147. Botkin, N.D.: Approximation schemes for finding the value function for differ-
ential games with nonterminal payoff functional. In: Schwerpunktprogramm der
Deutschen Forschungsgemeinschaft – Anwendungsbezogene Optimierung und
Steuerung. Report No. 439, pp. 1–15. Institut für Angewandte Mathematik und
Statistik der Universität Würzburg, Germany (1993)
148. Botkin, N.D.: Construction of viable sets for autonomous controlled systems. In:
Schwerpunktprogramm der Deutschen Forschungsgemeinschaft – Anwendungs-
bezogene Optimierung und Steuerung. Report No. 430, pp. 1–14. Institut für
Angewandte Mathematik und Statistik der Universität Würzburg, Germany
(1993)
149. Botkin, N.D.: Randomized algorithms for the separation of point sets and
for solving quadratic programs. In: Schwerpunktprogramm der Deutschen
Forschungsgemeinschaft – Anwendungsbezogene Optimierung und Steuerung.
Report No. 457, pp. 1–13. Institut für Angewandte Mathematik und Statistik
der Universität Würzburg, Germany (1993)
150. Botkin, N.D., Rjazantzeva, E.A.: Some examples of analytically constructed via-
bility kernels. In: Schwerpunktprogramm der Deutschen Forschungsgemeinschaft
– Anwendungsbezogene Optimierung und Steuerung. Report No. 515, pp. 1-16.
Mathematisches Institut der Technischen Universität München, Germany (1994)
151. Botkin, N.D., Stoer, J.: An algorithm for finding the minimum of a convex
function on the convex hull of a point set. In: Schwerpunktprogramm der
Deutschen Forschungsgemeinschaft – Anwendungsbezogene Optimierung und
Steuerung. Report No. 440, pp. 1–12. Institut für Angewandte Mathematik und
Statistik der Universität Würzburg, Germany (1993)
152. Botkin, N.D., Turova-Botkina, V.L.: An algorithm for finding the Chebyshev
center of a convex polyhedron. In: Schwerpunktprogramm der Deutschen
Forschungsgemeinschaft – Anwendungsbezogene Optimierung und Steuerung.
Report No. 395, pp. 1–11. Institut für Angewandte Mathematik und Statistik
der Universität Würzburg, Germany (1993)
153. Botkin, N.D.: Estimation of parameters of thin plates excited by piezoelectric
patches. Report TUM M9704, pp. 1–39. Technische Universität München,
Fakultät für Mathematik, München, Germany (1997)
154. Botkin, N.D.: Estimation of parameters of a linear thin plate excited by a piezo-
electric patch. Preprint 97-19, pp. 1–12. DFG project “Echtzeit-Optimierung
The Scientific Contribution of Nikolai D. Botkin xix
großer Systeme” (1997)
155. Botkin, N.D.: Parameters estimation of some electro-elasticity models. Preprint
97-18, pp. 1–8. DFG-Project “Echtzeit-Optimierung großer Systeme” (1997)
156. Hoffmann, K.-H., Botkin, N.D.: Oscillations of nonlinear thin plates excited
by piezoelectric patches. Preprint 97-17, pp. 1–13. DFG-Project “Echtzeit-
Optimierung großer Systeme” (1997)
157. Botkin, N.D.: Homogenization of an equation describing linear thin plates excited
by piezopatches. Preprint 98-1, pp. 1–12. DFG project “Echtzeit-Optimierung
großer Systeme” (1998)
158. Hoffmann, K.-H., Botkin, N.D.: Homogenization of equations describing vibration
of nonlinear thin plates excited by piezopatches. Preprint 98-18, pp. 1–20. DFG
project “Echtzeit-Optimierung großer Systeme” (1998)
159. Botkin, N.D., Litvinov, W.G., Rubezhansky, Y.I.: Models and problems for
piezoelectric elastic bodies and thin shells. Preprint 99-5, pp. 1–17. DFG-Project
“Echtzeit-Optimierung großer Systeme” (1999)
160. Botkin, N.D., Hoffmann, K.-H.: A fully coupled model of a nonlinear thin
plate excited by piezoelectric actuators. Preprint 00-25, pp. 1–13. DFG-Project
“Echtzeit-Optimierung großer Systeme” (2000)
161. Botkin, N.D., Hoffmann, K.-H.: Homogenization of a fully coupled model for
a nonlinear thin plate excited by piezoelectric transducers. Preprint 00-23,
pp. 1–11. DFG-Project “Echtzeit-Optimierung großer Systeme” (2000)
162. Hoffmann, K.-H., Botkin, N.D., Schlensog, M., Tewes, M., Turova, V.L.: Wave
propagation in biosensors. caesar Annual Report 2000, pp. 1–2. Nanotechnol-
ogy/Materials Science 2-1-3 (2001)
163. Hoffmann, K.-H., Botkin, N.D., Winzek, B.: Numerical modeling of shape mem-
ory composites. caesar Annual Report 2000, pp. 1–2. Nanotechnology/Materials
Science 2-1-2 (2001)
164. Botkin, N.D., Hoffmann, K.-H., Starovoitov, V.N.: Homogenization of interfaces
between rapidly oscillating fine elastic structures and fluids. Preprint 2002-12-30
30. caesar, Bonn (2002)
165. Botkin, N.D., Turova, V.L.: Mathematical models of a biosensor. Preprint
2002-12-30 31, pp. 1–18. caesar, Bonn (2002)
166. Hoffmann, K.-H., Botkin, N.D., Turova, V.L.: Biosensor: Modeling and simula-
tion. caesar Annual Report 2001, pp. 1–2. Coupling of Biological and Electronic
Systems 2-2-2 (2002)
167. Botkin, N.D., Hoffmann, K.-H., Meirmanov, A.M., Starovoitov, V.N.: Diffusion
problem with boundary conditions of hysteresis type. Preprint N111, pp. 1–15.
SFB611 “Singuläre Phänomene und Skalierung in mathematischen Modellen”,
Bonn (2003)
168. Botkin, N., Khludnev, A.: Shape optimization for elastic structures with non-
linear cracks. Preprint N121, pp. 1–15. SFB611 “Singuläre Phänomene und
Skalierung in mathematischen Modellen”, Bonn (2003)
169. Botkin, N.D., Turova, V.L.: Finite element modelling of a biosensor. Preprint
N110, pp. 1–19. SFB611 “Singuläre Phänomene und Skalierung in mathematis-
chen Modellen”, Bonn (2003)
xx
170. Hoffmann, K.-H., Botkin, N.D., Hölscher, H.: Tire sensor: Analysis and simu-
lation. caesar Annual Report 2002, pp. 1–2. Nanotechnology/Materials Science
2-1-2 (2003)
171. Hoffmann, K.-H., Botkin, N.D., Starovoitov, V.N., Turova, V.L.: Mathematical
modeling and simulation of the biosensor. caesar Annual Report 2002, pp. 1–2.
Coupling of Biological and Electronic Systems 2-2-2 (2003)
172. Hoffmann, K.-H., Botkin, N.D., Starovoitov, V.N., Turova, V.L.: Treatment
of the interface between fine elastic structures and fluids with homogenization
method. Preprint N100, pp. 1–24. SFB611 “Singuläre Phänomene und Skalierung
in mathematischen Modellen”, Bonn (2003)
173. Hoffmann, K.-H., Botkin, N.D., Turova, V.L.: Biosensor: Development of nu-
merical methods and software. caesar Annual Report 2002, pp. 1–2. Coupling of
Biological and Electronic Systems 2-2-3 (2003)
174. Botkin, N.D., Hoffmann, K.-H., Otto, F., Starovoitov, V.N, Turova, V.L.: Non-
linear interaction of piezoelectrically excited surface waves. Singular Phenomena
and Scaling in Mathematical Models. Arbeits- und Ergebnisbericht 2002–2004,
pp. 279–303. Reinsche Fridrich-Wilhelms-Universität, Sonderforschungsbereich
611, Bonn (2004)
175. Botkin, N.D., Melikyan, A.A., Turova, V.L.: Propagation of disturbances in
inhomogeneous anisotropic media. Preprint N181, pp. 1–25. SFB611 “Singuläre
Phänomene und Skalierung in mathematischen Modellen”, Bonn (2004)
176. Hoffmann, K.H, Botkin, N.D., Pykhteev, O.A., Kruz̆ik, M.: Orthodontic film
composites: Superelastic composite modeling. caesar Annual Report 2003,
pp. 1–2. Nanotechnology/Materials Science 2-1-1, Bonn (2004)
177. Hoffmann, K.-H., Botkin, N.D., Pykhteev, O.A., Turova, V.L.: MAMS: Mathe-
matical modeling of a biosensor. caesar Annual Report 2003, pp. 1–2. Coupling
of Biological and Electronic Systems 2-2-2, Bonn (2004)
178. Hoffmann, K.-H., Starovoitov, V.N., Botkin, N.D.: Modeling: Problems of
liquid-solid interaction and their application in biosensorics. caesar Annual
Report 2003, pp. 1–2. Coupling of Biological and Electronic Systems 2-2-1, Bonn
(2004)
179. Hölscher, H., Botkin, N., Tewes, M., Lohndorf, M., Hoffmann, K.-H., Quandt, E.:
Modelling of pneumatic tires by a finite element model for the developement of
a tire friction remote sensor. Preprint 2004-10-28 40, pp. 1–17. caesar, Bonn (2004)
180. Hoffmann, K.-H., Botkin, N.D., Pykhteev, O.A.: Orthodontic film composites:
Superelastic composite material. caesar Annual Report 2004, pp. 1–2. Nanotech-
nology/Materials Science 2-1-1, Bonn (2005)
181. Hoffmann, K.-H., Botkin, N.D., Pykhteev, O.A., Turova. V.L.: MAMS: Mathe-
matical modeling of a biosensor. caesar Annual Report 2004, pp. 1–2. Coupling
of Biological and Electronic Systems 2-2-1, Bonn (2005)
182. Hoffmann, K.-H., Starovoitov, V.N., Botkin, N.D.: Problems of particles sed-
imentation and their application in biosensorics. caesar Annual Report 2004,
pp. 1–2. Coupling of Biological and Electronic Systems 2-2-8, Bonn (2005)
183. Voigt, A., Hoffmann, K.-H., Backofen, R., Botkin, N., Goepfert, A., Pykhteev, O.,
Turova, V., Vey, S., Zollorsch, A.: Viola. caesar Annual Report 2004, pp. 1–2.
Nanotechnology/Materials Science 2-1-30, Bonn (2005)
The Scientific Contribution of Nikolai D. Botkin xxi
184. Hoffmann, K.-H., Botkin, N.D., Pykhteev, O.A.: Finite element modelling
of a microfluidic reactor. caesar Annual Report 2005, pp. 1–2. Nanotechnol-
ogy/Materials Science 2-1-28, Bonn (2006)
185. Hoffmann, K.-H., Botkin, N.D., Pykhteev, O.A.: Optimization of cooling proto-
cols in cryopreservation of living tissues. caesar Annual Report 2005, pp. 1–2.
Biotechnology 2-2-5, Bonn (2006)
186. Hoffmann, K.-H., Botkin, N.D., Pykhteev, O.A.: Orthodontic film composites-
superelastic composite material. caesar Annual Report 2005, pp. 1–2. Nanotech-
nology/Materials Science 2-1-12, Bonn (2006)
187. Hoffmann, D., Moske, M., Hoffmann, K.-H., Giersig, M., Pascal, R., Botkin, N.,
Starovoitov, V., Hilgendorff, M., Treitz, G., Zabe-Kuhn, M., Fassbender, B.:
ELOBIS–Elasto-optical biosensor based on nanostructures. caesar Annual Report
2005, pp. 1–2. Biotechnology 2-2-1, Boon (2006)
188. Voigt, A., Backofen, R., Botkin, N., Goepfert, A., Pykhteev, O., Starovoitova, B.,
Turova, V., Vey, S., Zollorsch, A.: VIOLA-TechSim. caesar Annual Report 2005,
pp. 1–2. Nanotechnogy/Materials Science 2-1-35, Bonn (2006)
189. Hoffmann, K.-H., Botkin, N.D., Egler, C., Fassbender, B., Hidendorff, M.,
Giersig, M., Knekties, J., Pascal, R., Patoka, P., Schuldenzucker, U.,
Troszczynska, S., Turova, V., Weckmann, A., Zabe-Kuhn, M.: Nanosafe2.
caesar Annual Report 2007, pp. 64–65. Molecular Biomedicine and Medical
Technology, Bonn (2007)
190. Botkin, N.D., Hoffmann, K.-H.: Optimal control in cryopreservation of cells
and tissues. Preprint SPP1253-10-07, pp. 1–34. DFG Priority programm 1253
“Optimization with Partial Differential Equations” (2008)
191. Botkin, N.D., Hoffmann, K.-H., Fraçkowiak, A., Cialkowski, A.M.: L2 and
H 1/2 fitting algorithms for solving inverse problems of heat transfer. Preprint
SPP1253-10-06, pp. 1–10. DFG Priority programm 1253 “Optimization with
Partial Differential Equations” (2008)
192. Botkin, N.D., Hoffmann, K.-H., Fraçkowiak, A., Cialkowski, A.M.: Study of the
heat transfer between gases and solid surfaces covered with micro rods. Preprint
SPP1253-10-05, pp. 1–13. DFG Priority programm 1253 “Optimization with
Partial Differential Equations” (2008)
193. Botkin, N.D., Hoffmann, K.-H., Mayer, N., Turova, V.L.: Approximation
schemes for solving disturbed control problems with nonterminal time and phase
constraints. Preprint SPP 1253-105, pp. 1–21. DFG Priority programm 1253
“Optimization with Partial Differential Equations” (2009)
194. Botkin, N.D., Hoffmann, K.-H., Turova, V.L.: Stable solutions of Hamilton-Jacobi
equations. Application to control of freezing processes. Preprint SPP1253-080,
pp. 1–25. DFG Priority programm 1253 “Optimization with Partial Differential
Equations” (2009)
195. Hoffmann, K.-H., Botkin, N.D., Amler, T.G., Witterstein, G., Mayer, N.:
Modeling of CO2 sequestration including parameter identification and numerical
simulations. Annual Report, KAUST-TUM Special Partnership, pp. 99–114.
Munich Centre of Advanced Computing, München (2010)
196. Kovtanyuk, A.E., Botkin, N.D., Hoffmann, K.-H.: Numerical simulations of
a coupled conductive-radiative heat transfer model using parallel computing.
xxii
Preprint SPP 1253-112, pp. 1–13. DFG Priority programm 1253 “Optimization
with Partial Differential Equations” (2010)
197. Hoffmann, K.-H., Botkin, N.D, Amler, T.G., Witterstein, G., Mayer, N.: Mod-
eling of CO2 sequestration including parameter identification and numerical
simulations. Annual Report, KAUST-TUM Special Partnership, pp. 127–148.
Munich Centre of Advanced Computing, München (2011)
198. Amler, T.G., Botkin, N.D., Hoffmann, K.-H., Hoteit, I.: Continuity in time
of solutions of a phase-field model. arXiv Preprint arXiv:1308.0157, pp. 1–17.
Cornell University (2013)
Conference Abstracts
199. Botkin, N.D., Patsko, V.S.: Universal optimal strategy in a differential game
with fixed terminal time. In: IV-th All-Union Conference on Optimal Control in
Mechanical Systems. Moscow, November 16–18, 1982. IPM AN SSSR, Moscow,
pp. 35–36 (1982) [in Russian]
200. Botkin, N.D., Patsko, V.S.: Universal strategy in a linear differential game. In:
IX-th All-Union Conference on Control Problems. Erevan, November 14–18,
1983. Nauka, Moscow, pp. 406–407 (1983) [in Russian]
201. Botkin, N.D., Patsko, V.S.: Numerical solution of linear differential games. In:
Third Conference on Differential Equations and Applications. Ruse, Bulgaria,
June 30–July 6, 1985. Center of Mathematics of the “Angel Kanchev” Higher
Technical School, Ruse, p. 22 (1985)
202. Botkin, N.D., Zarkh, M.A., Patsko, V.S.: Application of differential game theory
for solving of aircraft guaranteed control problems. In: All-Union Scientific-
Practice Conference: Safety and Efficiency of Exploiting of the Air Transport.
Reliability of the Aviation Technique. Leningrad - OLAGA, October 9–11, 1985.
Nauka, Moscow, p. 49 (1985) [in Russian]
203. Botkin, N.D., Zarkh, M.A., Patsko, V.S.: Numerical solving of low-dimensional
linear differential games with fixed terminal time. In: V-th All-Union Conference
on Control in Mechanical Systems. Kazan, June 12–14, 1985. Kazan Aviation
Institute, p. 34 (1985) [in Russian]
204. Botkin, N.D., Patsko, V.S., Taras’ev, A.M., Ushakov, V.N.: Approximate
solving of differential games. In: All-Union School-Seminar: Mathematical Mod-
elling in Science and Technology. Perm, June 9–15, 1986, p. 48 (1986) [in Russian]
205. Botkin, N.D., Kein, V.M., Patsko, V.S.: Nonlinear synthesis in the problem of
aircraft control on landing. In: Abstracts of the All-Union Seminar “Dynamics of
nonlinear control processes”. Tallinn, September 1987. Moscow, p. 135 (1987) [in
Russian]
206. Botkin, N.D., Krasov, A.I.: Optimal control of aircraft motion during runaway
acceleration under wind disturbances. In: XVI-th Gagarin Scientific Readings
on Astronautics and Aviation. Moscow, 1986. Nauka, Moscow, p. 93 (1987) [in
Russian]
207. Botkin, N.D.: Analytical construction of the value function in a pursuit-evasion
differential game with combined restrictions on the players’ controls. In: Confer-
ence of Young Mathematicians. Sverdlovsk, 1988. Scientific Reports, AN SSSR,
UrO, Sverdlovsk, p. 11 (1988) [in Russian]
The Scientific Contribution of Nikolai D. Botkin xxiii
208. Botkin, N.D., Patsko, V.S., Turova, V.L.: Simulation of the aircraft landing
process under windshear conditions. In: V-th All-Union Conference on Flight
Safety. Flight Safety and Preventing Aviation Accidents. Leningrad, November
1–3, 1988, p. 8 (1988) [in Russian]
209. Botkin, N.D., Zarkh, M.A.: Package of programs for solving linear differential
games of the second and third order. In: VI-th All-Union Conference on Optimal
Control in Mechanical Systems. Lvov, April 26–28, 1988, p. 175 (1988) [in Russian]
210. Botkin, N.D., Zhukov, S.P., Krasov, A.I.: Combined method of aircraft control on
landing. In: XVII-th Gagagin Scientific Readings on Austonautics and Aviation.
Moscow, 1988. Nauka, Moscow, p. 211 (1989) [in Russian]
211. Botkin, N.D., Zarkh, M.A.: Development and employment of a package of applied
programs for solving guaranteed control problems with the use of instrumental
system SATURN. In: Software for New Generation of Computers: 8th Sibirian
School on Packages of Applied Programs. Irkutsk, 1989. ICC SB RAS, Irkutsk,
p. 94 (1989) [in Russian]
212. Botkin, N.D., Patsko, V.S., Zarkh, M.A.: Numerical solving of linear differential
games. In: III-rd All-Union School-Seminar “Flight Dynamics and Operational
Research”. Klin, 1990. MAI, Moscow, pp. 103–104 (1990) [in Russian]
213. Botkin, N.D., Zarkh, M.A., Ivanov, A.G., Ryazantzeva, E.A.: Construction of a
solvability set for linear differential games. In: Abstracts of the VII-th All-Union
Conference “Control in Mechanical Systems”. Sverdlovsk, June 1990. Sverdlovsk,
p. 15 (1990) [in Russian]
214. Botkin, N.D., Patsko, V.S., Zarkh, M.A., Turova, V.L.: Methods for solving
non-smooth problems of conflict control. In: Abstracts of the International
Seminar “Non-smooth and Discontinuous Control and Optimization Problems”.
Vladivostok, 1991. Minsk, pp. 29-31 (1991) [in Russian]
215. Botkin, N.D., Zarkh, M.A., Kein, V.M., Patsko, V.S., Turova, V.L.: Synthesis
of guaranteeing aircraft control on take-off and landing. In: VIIth All-Union
Congress on Theoretical and Applied Mechanics. Moscow, August 15–21, 1991.
Moscow, p. 60 (1991) [in Russian]
216. Botkin, N.D., Zarkh, M.A., Patsko, V.S.: Optimal feedback control and switch
surfaces in linear differential games. In: International Conference on Game
Theory. Florence, Italy, June 25–27, 1991. Firenze (1991)
217. Botkin, N.D., Kein, V.M., Patsko, V.S., Turova, V.L., Zarkh, M.A.: Differential
games and aircraft control problems in the presence of wind disturbances. In:
IUTAM Symposium on Optimal Control of Mechanical Systems. Moscow, April
19–25, 1992. Moscow, pp. 9-10 (1992)
218. Botkin, N.D., Patsko, V.S., Turova, V.L., Zarkh, M.A.: Numerical methods for
solving differential games. Prospective applications to technical problems. In:
9th IFAC Workshop “Control Applications of Optimization”. München, FRG,
September 2–4, 1992, pp. 1–2 (1992)
219. Botkin, N.D., Zarkh, M.A., Patsko, V.S., Turova, V.L.: Numerical construction
of stability sets in linear differential games. In: International Seminar “Stability
and Oscillations of Nonlinear Control Systems”. Moscow, June 18–19, 1991, p. 84
(1992) [in Russian]
220. Botkin, N.D., Turova-Botkina, V.L.: An algorithm for finding the Chebyshev
center of a convex polyhedron. In: 16th IFIP Conference on System Modelling
xxiv
and Optimization. Compiegne, France, July 5–9, 1993. INRIA, vol. 2, pp. 635–637
(1993)
221. Botkin, N.D.: A randomized algorithm for solving quadratic programs. In:
J. Dolezal, J. Fidler (eds.) 17th IFIP TC7 Conference on System Modelling and
Optimization. Prague, Czech Republic, July 10–14, 1995. Institute of Information
Theory and Automation, Academy of Sciences of the Czech Republic, vol. 1,
pp. 317–320 (1995)
222. Botkin, N.: Identification of parameters for thermoelasticity models. In: Abstracts
of Symposium über Operations Research (SOR’95). Passau, Germany, September
13–15, 1995. Universität Passau, p. 111 (1995)
223. Botkin, N.: Parameters estimation of some electroelasticity models. In: Abstracts
of Symposium über Operations Research (SOR 96). Braunschweig, Germany,
September 4–6, 1996. Technische Universität Braunschweig, p. 114 (1996)
224. Botkin, N.D.: Differentiability of solutions of an electro-elasticity model w.r.t.
parameters. In: Abstracts of Invited Lectures and Short Communications
delivered at the Eighth International Colloquium on Differential Equations.
Plovdiv, Bulgaria, August 18–23, 1997, p. 38 (1997)
225. Botkin, N., Hoffmann, K.-H.: Mathematical models of structures controlled by
piezoelectric actuator. Design of real-time controls. In: SIAM Annual Meeting.
San Diego, California, July 9–13, 2001, p. 245 (2001)
226. Arndt, M., Botkin, N., Bourauel, C., Drescher, D., Hassdorf, R., Kruz̆ik, M.,
Moske, M., Pykhteev, O., Quandt, E., Rumpf, H., Sernetz, F., Sterzl, T.:
Analysis of force systems of superelastic nickel titanium alloy leveling arches
and development of superelastic compound wires for use in orthodontics. In:
Proceedings of the 6th International Symposium on Computer Methods in
Biomechanics & Biomechanical Engineering. Madrid, Spain, February 25–28,
2004 (2004)
227. Melikyan, A.A., Botkin, N.D., Turova, V.L.: Singularity phenomena in ray
propagation in anisotropic media. In: Second International Conference on
Physics and Control (PhysCon 2005). St. Petersburg, Russia, August 24–26,
2005, pp. 83–84 (2005)
228. Botkin, N.D., Hoffmann, K.-H., Turova, V.L.: Optimal control in cryopreser-
vation of living tissues. In: International Conference “Differential Equations
and Topology” dedicated to the Centennial Anniversary of Lev Semenovich
Pontryagin. Moscow, June 17–22, 2008, pp. 254–255 (2008)
229. Hoffmann, K.-H., Amler, T.G., Botkin, N.D., Turova, V.L.: Propagation and
deposition of air driven nanoparticles in complex channeled structures. Abstract
of poster presentation. In: Conference “Mathematics in Biosciences”, Helmholtz
Zentrum München, p. 32 (2008)
230. Hoffmann, K.-H., Botkin, N.D., Pykhteev, O.A.: Optimal control in cryop-
reservation of cells and tissues. Abstract of poster presentation. In: Conference
“Mathematics in Biosciences”, Helmholtz Zentrum München, p. 26 (2008)
231. Botkin, N.D., Hoffmann, K.-H.: Control design in cryopreservation of living cells.
In: International Conference “Actual Problems of Stability and Control Theory”.
Ekaterinburg, Russia, September 21–26, 2009, pp. 158–159 (2009)
232. Botkin, N.D., Turova, V.L.: Simulation of cell shrinkage caused by osmotic
cellular dehydration during freezing. In: 4th International Conference on High
The Scientific Contribution of Nikolai D. Botkin xxv
Performance Scientific Computing. Hanoi, Vietnam, March 2–6, 2009, p. 40 (2009)
233. Hoffmann, K.-H., Botkin, N.D.: Modeling and optimization in cryopreservation
using phase field models. In: 4th International Conference on High Performance
Scientific Computing. Hanoi, Vietnam, March 2–6, 2009, p. 88 (2009)
234. Botkin, N., Turova, V., Hoffmann, K.-H., Mayer, N.: Computation of value
functions in nonlinear differential games. In: 25th IFIP TC7 Conference on
System Modeling and Optimization. Berlin, Germany, September 12–16, 2011,
p. 236 (2011)
235. Kovtanyuk, A.E., Botkin, N.D., Hoffmann, K.-H.: Numerical simulations of a
coupled conductive-radiative heat transfer model. In: 5th International Confer-
ence on High Performance Scientific Computing. Hanoi, Vietnam, March 5–9,
2012, p. 119 (2012)
236. Botkin, N.D., Turova, V.L.: Application of Krasovskii’s unification method to
simulation of acoustic waves in anisotropic media. In: International Conference
“System Dynamics and Control Processes” dedicated to the 90th Anniversary
of Academician N. N. Krasovskii. Ekaterinburg, Russia, September 15–20, 2014,
pp. 228–229 (2014)
237. Botkin, N.D.: Mathematical modeling of physical processes in biology. In: Book
of abstracts of the 7th International Conference on Mathematical Modeling.
Yakutsk, Russia, June 30–July 4, 2014, pp. 4–5 (2014)
238. Kovtanyuk, A.E., Chebotarev, A.Y., Botkin, N.D., Hoffmann, K.-H.: Optimal
control in a model of complex heat transfer. In: Dynamics and Structure of
Combustion Waves: 2nd International Conference. Vladivostok, Russia, July
23–27, 2014, p. 20 (2014)
239. Kovtanyuk, A.E., Chebotarev, A.Y., Botkin, N.D., Hoffmann, K.-H.: Unique
solvability of a P1 steady-state heat transfer model in three dimensions. In:
Dynamics and Structure of Combustion Waves: 2nd International Conference.
Vladivostok, Russia, July 23-27, 2014, p. 12 (2014)
240. Turova, V.L., Lampe, R., Botkin, N.D., Blumenstein, T., Alves-Pinto, A.: Au-
toregulation of cerebral blood flow: Towards preventing intracranial hemorrhages
in premature newborns. In: Book of abstracts of the 7th International Conference
on Mathematical Modeling. Yakutsk, Russia, June 30–July 4, 2014, pp. 87–88
(2014)
241. Lampe, R., Botkin, N., Turova, V., Blumenstein, T., Alves-Pinto, A.: Cerebral
blood circulation in premature infants by means of mathematical modeling.
In: Abstracts of the 41st Annual Meeting of the Society of Neuropedi-
atrics. Basel, April 23–26, 2015. Neuropediatrics 46(S 01), FV01-03 (2015).
https://doi.org/10.1055/s-0035-1550640
242. Botkin, N.D., Turova, V.L.: Dynamic games in biomedical problems. In: 11th
ISDG Workshop. Warsaw, Poland, July 13–15, 2017, p. 1 (2017)
243. Kovtanyuk, A.E., Chebotarev, A.Yu., Botkin, N.D., Turova, V.L., Sidorenko, I.N.,
Lampe, R.: An inverse problem of oxygen transport in brain. In: The 32nd Inter-
national Conference of the Jangjeon Mathematical Society (ICJMS2019). Vladi-
vostok, Russia, July 17–21, 2019, pp. 47–50 (2019)
Varvara Turova, Technical University of Munich