Theory and numerical methods of solving inverse and ill-posed problems of Natural sciences.
Main publications:
S.I. Kabanikhin, A.D. Satybaev, M.A. Shishlenin, Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems, VSP, Utrecht, Boston, 2004, 180 pp.
P. S. Surnin, M. A. Shishlenin, G. A. Bocharov, “Determination of the parameters of the mathematical model of the immune response to HIV”, Nonlocal and nonlinear problems, CMFD, 71, no. 1, PFUR, M., 2025, 159–175
2024
2.
Mikhail V. Bezgachev, Maxim A. Shishlenin, Alexander V. Sokolov, “Identification of a mathematical model of economic development of two regions of the world”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 47 (2024), 12–30;
3.
D. V. Klyuchinskiy, N. S. Novikov, M. A. Shishlenin, “On the numerical reconstruction of the three-dimensional density of the medium in the acoustic system of equations”, Sib. elektron. matem. izv., 21:2 (2024), 82–98;
2023
4.
M. A. Shishlenin, N. A. Savchenko, N. S. Novikov, D. V. Klyuchinskiy, “On the reconstruction of the absorption coefficient for the 2D acoustic system”, Sib. elektron. matem. izv., 20:2 (2023), 1474–1489;
R. L. Argun, A. V. Gorbachev, D. V. Lukyanenko, M. A. Shishlenin, “Features of numerical reconstruction of a boundary condition in an inverse problem for a reaction–diffusion–advection equation with data on the position of a reaction front”, Comput. Math. Math. Phys., 62:3 (2022), 441–451
2021
6.
A. S. Kozelkov, O. L. Krutyakova, V. V. Kurulin, D. Yu. Strelets, M. A. Shishlenin, “The accuracy of numerical simulation of the acoustic wave propagations in a liquid medium based on Navier-Stokes equations”, Sib. elektron. matem. izv., 18:2 (2021), 1238–1250;
O. I. Krivorotko, S. I. Kabanikhin, N. Yu. Zyatkov, A. Yu. Prikhodko, N. M. Prokhoshin, M. A. Shishlenin, “Mathematical modeling and forecasting of COVID-19 in
Moscow and Novosibirsk region”, Num. Anal. Appl., 13:4 (2020), 332–348
8.
S. I. Kabanikhin, I. M. Kulikov, M. A. Shishlenin, “An algorithm for recovering the characteristics of the initial state of supernova”, Comput. Math. Math. Phys., 60:6 (2020), 1008–1016
2019
9.
D. V. Lukyanenko, V. B. Grigorev, V. T. Volkov, M. A. Shishlenin, “Solving of the coefficient inverse problem for a nonlinear singularly perturbed two-dimensional reaction–diffusion equation with the location of moving front data”, Computers and Mathematics with Applications, 77:5 (2019), 1245–1254
A. Belonosov, M. Shishlenin, D. Klyuchinskiy, “A comparative analysis of numerical methods of solving the continuation problem for 1D parabolic equation with the data given on the part of the boundary”, Advances in Computational Mathematics, 45:2 (2019), 735–755
M. A. Shishlenin, S. E. Kasenov, Z. A. Askerbekova, “Numerical algorithm for solving the inverse problem for the Helmholtz equation”, Communications in Computer and Information Science, 998 (2019), 197–207
V. M. Isakov, S. I. Kabanikhin, A. A. Shananin, M. A. Shishlenin, S. Zhang, “Algorithm for determining the volatility function in the black–scholes model”, Comput. Math. Math. Phys., 59:10 (2019), 1753–1758
2018
13.
D. V. Lukyanenko, M. A. Shishlenin, V. T. Volkov, “Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data”, Communications in Nonlinear Science and Numerical Simulation, 54 (2018), 1339–1351
S. I. Kabanikhin, M. A. Shishlenin, “Recovery of the time-dependent diffusion coefficient by known non-local data”, Num. Anal. Appl., 11:1 (2018), 38–44
D. N. Hào, L. T. Thu Giang, S. Kabanikhin, M. Shishlenin, “A finite difference method for the very weak solution to a Cauchy problem for an elliptic equation”, Journal of Inverse and Ill-Posed Problems, 26:6 (2018), 835–857
S. I. Kabanikhin, K. T. Iskakov, B. B. Sholpanbaev, M. A. Shishlenin, D. K. Tokseit, “Development of a mathematical model for signal processing using laboratory data”, Bulletin of the Karaganda University-Mathematics, 92:4 (2018), 148–157
N. S. Novikov, S. I. Kabanikhin, M. A.Shishlenin, “Direct method for solving coefficient inverse problems of seismics and acoustics”, Funktsionalnye prostranstva. Differentsialnye operatory. Problemy matematicheskogo obrazovaniya. Tezisy dokladov Pyatoi Mezhdunarodnoi konferentsii, posvyaschennoi 95-letiyu so dnya rozhdeniya chlenakorrespondenta RAN, akademika Evropeiskoi akademii nauk L.D. Kudryavtseva. (Rossiiskii universitet druzhby narodov. 26-29 noyabrya 2018.), Rossiiskii universitet druzhby narodov., Moskva, 2018, 238
20.
Kabanikhin S.I., Novikov N.S., Shishlenin M.A., “Svedenie obratnoi zadachi dlya uravneniya kolebanii k sisteme integralnykh uravnenii pervogo roda”, Trudy Mezhdunarodnoi konferentsii “Vychislitelnaya matematika i matematicheskaya geofizika” posvyaschennaya 90-letiyu so dnya rozhdeniya akademika A. S. Alekseeva ("Akademgorodok, Novosibirsk, 8–10 oktyabrya 2018 g."), Institut vychislitelnoi matematiki i matematicheskoi geofiziki SO RAN, Novosibirsk, 2018, 163–169
21.
Prikhodko A.Yu., Shishlenin M.A., Stadnichenko O.A., “Opredelenie skorostei khimicheskikh reaktsii v piroliticheskom reaktore”, Trudy Mezhdunarodnoi konferentsii “Vychislitelnaya matematika i matematicheskaya geofizika” posvyaschennaya 90-letiyu so dnya rozhdeniya akademika A. S. Alekseeva ("Akademgorodok, Novosibirsk, 8–10 oktyabrya 2018 g."), Institut vychislitelnoi matematiki i matematicheskoi geofiziki SO RAN, 2018, 323–331
22.
M. A. Shishlenin, “Mikroseismicheskii monitoring gidrorazryva plasta”, Trudy Mezhdunarodnoi konferentsii “Vychislitelnaya matematika i matematicheskaya geofizika” posvyaschennaya 90-letiyu so dnya rozhdeniya akademika A. S. Alekseeva ("Akademgorodok, Novosibirsk, 8–10 oktyabrya 2018 g."), Institut vychislitelnoi matematiki i matematicheskoi geofiziki SO RAN, 2018, 407–413
23.
M. A. Shishlenin, S. V. Golovin, “Opredelenie koeffitsienta parabolicheskogo uravneniya po dopolnitelnoi informatsii, zadannoi v diskretnom nabore tochek vnutri oblasti”, Trudy Mezhdunarodnoi konferentsii “Vychislitelnaya matematika i matematicheskaya geofizika” posvyaschennaya 90-letiyu so dnya rozhdeniya akademika A. S. Alekseeva ("Akademgorodok, Novosibirsk, 8–10 oktyabrya 2018 g."), Institut vychislitelnoi matematiki i matematicheskoi geofiziki SO RAN, 2018, 414–418
24.
S. Kabanikhin, M. Shishlenin, N. Novikov, “Multidimensional analogs of Gelfand-Levitan-Krein equations”, Proceedings of the 6th International Conference on Control and Optimization with Industrial Applications (Baku, Azerbaijan, July 11-13, 2018), 1, eds. A. Fikret, B. Tamer, Baku State University, Institute of Applied Mathematics, Baku, 2018, 31–33
25.
S. Kabanikhin, N. Novikov, M. Shishlenin, “Linear seismic data processing of area observing systems”, Proceedings of the 6th International Conference on Control and Optimization with Industrial Applications (Baku, Azerbaijan, July 11–13, 2018), 1, eds. A. Fikret, B. Tamer, Baku State University, Institute of Applied Mathematics, Baku, 2018, 219–221
2017
26.
Belonosov A., Shishlenin M., “Regularization methods of the continuation problem for the parabolic equation”, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 10187 LNCS (2017), 220–226
A. Yu. Prikhodko, M. A Shishlenin, “Sravnitelnyi analiz chislennykh metodov opredeleniya debita skvazhiny i obvodnennosti po dopolnitelnym izmereniyam davleniya i temperatury”, Trudy Mezhdunarodnoi nauchnoi konferentsii Marchukovskie nauchnye chteniya - 2017. (Novosibirsk, 25 iyunya-14 iyulya 2017 g.), Institut vychislitelnoi matematiki i matematicheskoi geofiziki SO RAN, Novosibirsk, 2017, 705-710
28.
S.I. Kabanikhin, M.A. Shishlenin, B.B. Sholpanbaev, “Chislennoe reshenie nachalno-kraevoi zadachi dlya uravneniya elektrodinamiki”, Trudy mezhdunarodnoi shkoly-konferentsii “Sobolevskie chteniya”. (Institut matematiki im. S.L. Soboleva SO RAN, Novosibirsk, 20-23 avgusta 2017 g.), Institut matematiki im. S.L. Soboleva SO RAN, Novosibirsk, 2017, 62-63
29.
G.G. Lazareva, M.A. Shishlenin, R.A. Idiyatullin, E.A. Fedorov, V.B. Zavolzhskii, I.V. Khlestov, “Pryamaya i obratnaya zadacha kompleksnogo vozdeistviya na plast s primeneniem tekhnologii TGKhV BS”, Trudy Mezhdunarodnoi nauchnoi konferentsii Marchukovskie nauchnye chteniya - 2017. (Novosibirsk, 25 iyunya-14 iyulya 2017 g.), Institut vychislitelnoi matematiki i matematicheskoi geofiziki SO RAN, 2017, 514-520
30.
S. I. Kabanikhin, M. A Shishlenin, “Koeffitsientnye obratnye zadachi dlya parabolicheskikh uravnenii s dannymi vnutri oblasti”, Trudy Mezhdunarodnoi nauchnoi konferentsii Marchukovskie nauchnye chteniya - 2017. (Novosibirsk, 25 iyunya-14 iyulya 2017 g.), Institut vychislitelnoi matematiki i matematicheskoi geofiziki SO RAN, 2017, 370-372
31.
S. I. Kabanikhin, M. A Shishlenin, “Vosstanovlenie koeffitsientov, zavisyaschikh ot vremeni, v dinamicheskikh obratnykh zadachakh po nelokalnym dannym”, Trudy Mezhdunarodnoi nauchnoi konferentsii Marchukovskie nauchnye chteniya - 2017. (Novosibirsk, 25 iyunya-14 iyulya 2017 g.), Institut vychislitelnoi matematiki i matematicheskoi geofiziki SO RAN, 2017, 364-369
32.
S. I. Kabanikhin, N. S. Novikov, M. A Shishlenin, “Ob odnoi modifikatsii uravneniya Gelfanda–Levitana”, Trudy Mezhdunarodnoi nauchnoi konferentsii Marchukovskie nauchnye chteniya - 2017. (Novosibirsk, 25 iyunya-14 iyulya 2017 g.), Institut vychislitelnoi matematiki i matematicheskoi geofiziki SO RAN, 2017, 357-363
33.
S. I. Kabanikhin, I. M. Kulikov, M. A Shishlenin, “O metode vysokogo poryadka tochnosti dlya resheniya pryamykh i obratnykh zadach gravitatsionnoi gazovoi dinamiki v sfericheskoi simmetrii”, Trudy Mezhdunarodnoi nauchnoi konferentsii Marchukovskie nauchnye chteniya - 2017. (Novosibirsk, 25 iyunya-14 iyulya 2017 g.), Institut vychislitelnoi matematiki i matematicheskoi geofiziki SO RAN, 2017, 348-356
34.
G. Bakanov, S. Kabanikhin, N. Novikov, M. Shishlenin, “On the solvability of the discrete analogue of Gelfand–Levitan equation”, Trudy Mezhdunarodnoi nauchnoi konferentsii Marchukovskie nauchnye chteniya - 2017. (Novosibirsk, 25 iyunya-14 iyulya 2017 g.), Institut vychislitelnoi matematiki i matematicheskoi geofiziki SO RAN, 2017, 1118-1122
2016
35.
Titarenko S.S., Kulikov I.M., Chernykh I.G., Shishlenin M.A., Krivorot’Ko O.I., Voronov D.A., Hildyard M., “Multilevel parallelization: Grid methods for solving direct and inverse problems”, Communications in Computer and Information Science, 687 (2016), 118–131
S.I. Kabanikhin, M.A. Shishlenin, “Two-dimensional analogs of the equations of Gelfand, Levitan, Krein, and Marchenko”, Eurasian Journal of Mathematical and Computer Applications, 3:2 (2015), 70–99
40.
Kabanikhin S.I., Sabelfeld K.K., Novikov N.S., Shishlenin M.A., “Numerical solution of an inverse problem of coefficient recovering for a wave equation by a stochastic projection methods”, Monte Carlo Methods and Applications, 21:3 (2015), 189–203
S.I. Kabanikhin, M.A. Shishlenin, “Multidimensional analogues of Gelfand-Levitan, Marchenko and Krein equations. Theory, numerics and applications”, Vychislitelnye tekhnologii, 20:3 (2015), 63–69
43.
S.I. Kabanikhin, M. Bektemesov, M.A. Shishlenin, “The size of the domain of measurements is the regularization parameter in continuation problem”, Vychislitelnye tekhnologii, 20:3 (2015), 130–136
44.
S. I. Kabanikhin, M. A. Shishlenin, “Two-dimensional analogs of the equations of Gelfand, Levitan, Krein, and Marchenko”, Eurasian Journal of Mathematical and Computer Applications, 3:2 (2015), 70–99
2014
45.
M. A. Shishlenin, “The matrix method in inverse source problems”, Sib. Èlektron. Mat. Izv., 11 (2014), 161–171
46.
D. B. Nurseitov, M. A. Shishlenin, B. B. Sholpanbaev, “Two dimensional linearized inverse problems”, Sib. Èlektron. Mat. Izv., 11 (2014), 145–155
47.
A. S. Belonosov, M. A. Shishlenin, Sib. Èlektron. Mat. Izv., 11 (2014), 22–34
48.
S. I. Kabanikhin, M. A. Shishlenin, “Proceedings of the V International scientific school-conference for young scientists “Theory and numerical methods for solving inverse and ill-posed problem””, Sib. Èlektron. Mat. Izv., 11 (2014), 1–171
49.
Kabanikhin S.I., Shishlenin M.A., Nurseitov D.B., Nurseitova A.T., Kasenov S.E., “Comparative Analysis of Methods for Regularizing an Initial Boundary Value Problem for the Helmholtz Equation”, Journal of Applied Mathematics, 2014 (2014), 786326 , 7 pp.
S.I. Kabanikhin, M.A. Shishlenin, “Regularization of the decision prolongation problem for parabolic and elliptic elliptic equations from border part”, Eurasian Journal of Mathematical and Computer Applications, 2:2 (2014), 81–91
2013
51.
S. I. Kabanikhin, O. I. Krivorotko, M. A. Shishlenin, “A numerical method for solving inverse thermoacoustic problem”, Num. Anal. Appl., 6:1 (2013), 34–39
52.
S. I. Kabanikhin, M. A. Shishlenin, “Proceedings of the IV International scientific school-conference for young scientists “Theory and numerical methods for solving inverse and ill-posed problem”. Part I”, Sib. Èlektron. Mat. Izv., 10 (2013), 1–86
53.
Kabanikhin S.I., Gasimov Y.S., Nurseitov D.B., Shishlenin M.A., Sholpanbaev B.B., Kasenov S., “Regularization of the continuation problem for elliptic equations”, Journal of Inverse and Ill-Posed Problems, 21:6 (2013), 871–884
S.I. Kabanikhin, M.A. Shishlenin, “Stability analysis of a continuation problem for the Helmholtz equation”, Bulletin of the Novosibirsk Computing Center. Series: Mathemaical Modeling in Geophysics, 16 (2013), 59-68
2012
57.
S. I. Kabanikhin, M. A. Shishlenin, “On the use of a priori information in coefficient inverse problems for hyperbolic equations”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 1, 2012, 147–164
58.
S.I. Kabanikhin, K.T. Iskakov, M.A. Bektemesov, M.A. Shishlenin, Algoritmy i chislennye metody resheniya obratnykh i nekorrektnykh zadach, KazNPU, Astana, Kazakhstan, 2012
59.
S.I. Kabanikhin, M.A. Bektemesov, M.A. Shishlenin, Metody resheniya nekorrektnykh zadach lineinoi algebry, KazNPU, Almaty, Kazakhstan, 2012
60.
S.I. Kabanikhin, M.A. Shishlenin, “Numerical Methods for Solving Inverse Hyperbolic Problems”, Computational Methods for Applied Inverse Problems, eds. Wang Y., Yagola A.G., Yang C., de Gruyter, 2012, 369–394
S. I. Kabanikhin, A. N. Cheremisin, M. A. Shishlenin, “The inverse problem of determining stream watering and discharge in a vertical flowing well”, Sib. Zh. Ind. Mat., 14:3 (2011), 31–36
62.
M. I. Epov, S. I. Kabanikhin, V. L. Mironov, K. V. Muzalevskii, M. A. Shishlenin, “A comparative analysis of two methods for calculating electromagnetic fields in the near-well space of oil and gas collectors”, Sib. Zh. Ind. Mat., 14:2 (2011), 132–138
63.
S.I. Kabanikhin, M.A. Shishlenin, “Numerical algorithm for two-dimensional inverse acoustic problem based on Gel'fand-Levitan-Krein equation”, Journal of Inverse and Ill-Posed Problems, 18:9 (2011), 979–995
S. I. Kabanikhin, A. N. Cheremisin, M. A. Shishlenin, “Finite element method for Helmholtz equation”, Sib. Èlektron. Mat. Izv., 7 (2010), 362–379
69.
V. G. Romanov, S. I. Kabanikhin, M. A. Shishlenin, “Investigation of mathematical model of electromagnetic probe in axially symmetrical borehole”, Sib. Èlektron. Mat. Izv., 7 (2010), 307–321
70.
S. I. Kabanikhin, M. A. Shishlenin, “Direct methods for solving inverse acoustic problems”, Sib. Èlektron. Mat. Izv., 7 (2010), 199–206
71.
M. A. Shishlenin, “Direct method for solving inverse acoustic problems”, Sib. Èlektron. Mat. Izv., 7 (2010), 123–129
72.
S. I. Kabanikhin, M. A. Shishlenin, “Proceedings of the first international scientific school-conference for young scientists “Theory and numerical methods for solving inverse and ill-posed problem”, Part I”, Sib. Èlektron. Mat. Izv., 7 (2010), 1–394
2008
73.
S. I. Kabanikhin, M. A. Shishlenin, “Direct and iteration methods for solving inverse and ill-posed problems”, Sib. Èlektron. Mat. Izv., 5 (2008), 595–608
74.
S.I. Kabanikhin, M.A. Shishlenin, “Quasi-solution in inverse coefficient problems”, Journal of Inverse and Ill-Posed Problems, 16:7 (2008), 705–713
Beilina L., Shishlenin M.A., Computational Comparison of Adaptive Hybrid FEM/FDM Method and Gel'Fand-Levitan-Krein Method for an Inverse Scattering Problem, Preprints of Math. Department of Basel University, Basel University, Basel, 2006
2004
76.
S.I. Kabanikhin, M.A. Shishlenin, “Boundary control and Gel’fand-Levitan-Krein methods in inverse acoustic problem”, Journal of Inverse Ill-Posed Problem, 12:2 (2004), 125–144
S.I. Kabanikhin, A.D. Satybaev, M.A. Shishlenin, Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems, VSP, Utrecht, Boston, 2004 , 180 pp.
2003
78.
S. I. Kabanikhin, O. Scherzer, M. A. Shishlenin, “Iteration methods for solving a two dimensional inverse problem for a hyperbolic equation”, Journal of Inverse and Ill-Posed Problems, 11:1 (2003), 87–109
S.I. Kabanikhin, M.A. Shishlenin, “Comparative analysis of boundary control and Gel'fand-Levitan methods of solving inverse acoustic problem”, Inverse Problems in Engineering Mechanics IV, Elsevier, 2003, 503–512
Inverse problems of acoustical tomography M. A. Shishlenin, S. I. Kabanikhin, N. S. Novikov The ninth international conference "Quasilinear Equations, Inverse Problems and their Applications" (QIPA 2023) December 4, 2023 17:40
2.
Обратные задачи электроакустической медицинской томографии: численные методы и глубокое обучение M. A. Shishlenin VI International Conference "Function Spaces. Differential Operators. Problems of Mathematical Education", dedicated to the centennial anniversary of the corresponding member of Russian Academy of Sciences, academician of European Academy of Sciences L.D. Kudryavtsev November 15, 2023 16:30
2025
