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.
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
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
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
5.
Kabanikhin S.I., Nurseitov D.B., Shishlenin M.A., Sholpanbaev B.B., “Inverse problems for the ground penetrating radar”, Journal of Inverse and Ill-Posed Problems, 21:6 (2013), 885–892
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
9.
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, 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, “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
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
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, “Boundary control and Gel’fand-Levitan-Krein methods in inverse acoustic problem”, Journal of Inverse Ill-Posed Problem, 12:2 (2004), 125–144
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
16.
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
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
18.
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
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
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
22.
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
23.
M. A. Shishlenin, “The matrix method in inverse source problems”, Sib. Èlektron. Mat. Izv., 11 (2014), 161–171
24.
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
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
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;
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
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
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
32.
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
33.
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
34.
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
35.
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
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, “Finite element method for Helmholtz equation”, Sib. Èlektron. Mat. Izv., 7 (2010), 362–379
39.
M. A. Shishlenin, “Direct method for solving inverse acoustic problems”, Sib. Èlektron. Mat. Izv., 7 (2010), 123–129
40.
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
41.
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
42.
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
43.
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
44.
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
45.
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
46.
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
47.
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
48.
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
49.
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
50.
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
51.
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
52.
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
53.
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
54.
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
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
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
59.
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
60.
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
61.
D. B. Nurseitov, M. A. Shishlenin, B. B. Sholpanbaev, “Two dimensional linearized inverse problems”, Sib. Èlektron. Mat. Izv., 11 (2014), 145–155
62.
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
63.
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
64.
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
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
67.
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
68.
S.I. Kabanikhin, M.A. Bektemesov, M.A. Shishlenin, Metody resheniya nekorrektnykh zadach lineinoi algebry, KazNPU, Almaty, Kazakhstan, 2012
S. I. Kabanikhin, M. A. Shishlenin, “Direct methods for solving inverse acoustic problems”, Sib. Èlektron. Mat. Izv., 7 (2010), 199–206
73.
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
74.
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
75.
S.I. Kabanikhin, A.D. Satybaev, M.A. Shishlenin, Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems, VSP, Utrecht, Boston, 2004 , 180 pp.
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;
81.
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;
82.
M.A. Shishlenin, “Fourth International Scientific School-Conference for Young Scientists “Theory and Computational Methods for Inverse and Ill-Posed Problems””, Journal of Inverse and Ill-Posed Problems, 20:1 (2012), 133–136
83.
M.A. Shishlenin, “Third International Scientific Conference and Young Scientists School “Theory and Computational Methods for Inverse and Ill-Posed Problems””, Journal of Inverse and Ill-Posed Problems, 19:3 (2011), 545–548
84.
C. Clason, M.A. Shishlenin, “Recent advances in analytical and numerical methods in inverse problems for PDEs (minisymposium report)”, Journal of Inverse and Ill-Posed Problems, 18:9 (2011), 955–958
85.
Anikonov Y.E., Bakushinskii A.B., Goncharsky A.V., Hasanov A., Kabanikhin S.I., Lavrentiev M.M., Romanov V.G., Shishlenin M.A., Tanana V.P., Tikhonravov A.V., Vasin V.V., Yagola A.G., “Michael V. Klibanov”, Journal of Inverse and Ill-Posed Problems, 19:3 (2011), 533–536
Presentations in Math-Net.Ru
1.
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
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