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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2018, Volume 21, Number 1, Pages 55–63
DOI: https://doi.org/10.15372/SJNM20180104
(Mi sjvm668)
 

This article is cited in 25 scientific papers (total in 25 papers)

Recovery of the time-dependent diffusion coefficient by known non-local data

S. I. Kabanikhinabc, M. A. Shishleninabc

a Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 6 Lavrentiev av., Novosibirsk, 630090, Russia
b Sobolev Institute of Mathematics SB RAS, 4 Acad. Koptyug av., Novosibirsk, 630090, Russia
c Novosibirsk State University, 2 Pirogova str., Novosibirsk, 630090, Russia
References:
Abstract: The inverse problem of recovering the leading time-dependent coefficient by the known non-local additional information is investigated. For an approximate solution of the nonlinear inverse problems we propose the gradient method of minimizing the target functional. The comparative analysis with the method based on the linearized approximation scheme with respect to time is made. The results of the numerical calculations are presented.
Key words: parabolic equation, time-dependent coefficient inverse problem, numerical methods, nonlocal condition.
Funding agency Grant number
Russian Foundation for Basic Research 17-51-540004
16-29-15120
16-01-00755
Received: 16.06.2017
Revised: 07.07.2017
English version:
Numerical Analysis and Applications, 2018, Volume 11, Issue 1, Pages 38–44
DOI: https://doi.org/10.1134/S1995423918010056
Bibliographic databases:
Document Type: Article
UDC: 519.633
Language: Russian
Citation: S. I. Kabanikhin, M. A. Shishlenin, “Recovery of the time-dependent diffusion coefficient by known non-local data”, Sib. Zh. Vychisl. Mat., 21:1 (2018), 55–63; Num. Anal. Appl., 11:1 (2018), 38–44
Citation in format AMSBIB
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Linking options:
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  • This publication is cited in the following 25 articles:
    1. Y. R. Ashrafova, “An Inverse Parametric Problem for a Large System of Differential Equations with Nonlocal Boundary Conditions”, Numer. Analys. Appl., 18:1 (2025), 1  crossref
    2. Ali Ugur Sazaklioglu, “An iterative numerical method for an inverse source problem for a multidimensional nonlinear parabolic equation”, Applied Numerical Mathematics, 198 (2024), 428  crossref
    3. D. V. Lukyanenko, R. L. Argun, A. A. Borzunov, A. V. Gorbachev, V. D. Shinkarev, M. A. Shishlenin, A. G. Yagola, “On the Features of Numerical Solution of Coefficient Inverse Problems for Nonlinear Equations of the Reaction–Diffusion–Advection Type with Data of Various Types”, Diff Equat, 59:12 (2023), 1734  crossref
    4. S. Z. Dzhamalov, B. K. Sipatdinova, “Semi-Nonlocal Boundary Problem for a Three-Dimensional Second Kind Mixed Equation in a Unbounded Parallelepiped”, Lobachevskii J Math, 44:3 (2023), 1145  crossref
    5. Sergey Kabanikhin, Maxim Shishlenin, Nikita Novikov, Nikita Prokhoshin, “Spectral, Scattering and Dynamics: Gelfand–Levitan–Marchenko–Krein Equations”, Mathematics, 11:21 (2023), 4458  crossref
    6. 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  mathnet  mathnet  crossref  crossref  isi  scopus
    7. R.L. Argun, V.T. Volkov, D.V. Lukyanenko, “Numerical simulation of front dynamics in a nonlinear singularly perturbed reaction–diffusion problem”, Journal of Computational and Applied Mathematics, 412 (2022), 114294  crossref
    8. T. K. Yuldashev, O. Sh. Kilichev, “Nonlinear Inverse Problem for a Sixth Order Differential Equation with Two Redefinition Functions”, Lobachevskii J Math, 43:3 (2022), 804  crossref
    9. K. R. Aida-zade, Y. R. Ashrafova, “Control of effects in the right-hand sides of a large ODE system of a block structure and optimization of sources in unseparated boundary conditions”, Num. Anal. Appl., 14:3 (2021), 201–219  mathnet  crossref  crossref  isi
    10. T. K. Yuldashev, “Obratnaya smeshannaya zadacha dlya integro-differentsialnogo uravneniya s mnogomernym operatorom Benni—Lyuka i nelineinymi maksimumami”, Differentsialnye uravneniya, geometriya i topologiya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 201, VINITI RAN, M., 2021, 3–15  mathnet  crossref
    11. R. Argun, A. Gorbachev, D. Lukyanenko, M. Shishlenin, “On some features of the numerical solving of coefficient inverse problems for an equation of the reaction-diffusion-advection-type with data on the position of a reaction front”, Mathematics, 9:22 (2021), 2894  crossref  isi  scopus
    12. R. Argun, A. Gorbachev, N. Levashova, D. Lukyanenko, “Inverse problem for an equation of the reaction-diffusion-advection type with data on the position of a reaction front: features of the solution in the case of a nonlinear integral equation in a reduced statement”, Mathematics, 9:18 (2021), 2342  crossref  isi  scopus
    13. D. V. Klyuchinskiy, N. S. Novikov, M. A. Shishlenin, “CPU-time and RAM memory optimization for solving dynamic inverse problems using gradient-based approach”, J. Comput. Phys., 439 (2021), 110374  crossref  mathscinet  isi  scopus
    14. N. Levashova, A. Gorbachev, R. Argun, D. Lukyanenko, “The problem of the non-uniqueness of the solution to the inverse problem of recovering the symmetric states of a bistable medium with data on the position of an autowave front”, Symmetry-Basel, 13:5 (2021), 860  crossref  isi  scopus
    15. D. V. Lukyanenko, A. A. Borzunov, M. A. Shishlenin, “Solving coefficient inverse problems for nonlinear singularly perturbed equations of the reaction-diffusion-advection type with data on the position of a reaction front”, Commun. Nonlinear Sci. Numer. Simul., 99 (2021), 105824  crossref  mathscinet  isi  scopus
    16. D. Lukyanenko, T. Yeleskina, I. Prigorniy, T. Isaev, A. Borzunov, M. Shishlenin, “Inverse problem of recovering the initial condition for a nonlinear equation of the reaction-diffusion-advection type by data given on the position of a reaction front with a time delay”, Mathematics, 9:4 (2021), 342  crossref  isi  scopus
    17. T. K. Yuldashev, F. D. Rakhmonov, “On a Benney–Luke Type Differential Equation with Nonlinear Boundary Value Conditions”, Lobachevskii J Math, 42:15 (2021), 3761  crossref
    18. D. V. Lukyanenko, I. V. Prigorniy, M. A. Shishlenin, “Some features of solving an inverse backward problem for a generalized Burgers' equation”, J. Inverse Ill-Posed Probl., 28:5 (2020), 641–649  crossref  mathscinet  zmath  isi  scopus
    19. D. V. Lukyanenko, M. A. Shishlenin, V. T. Volkov, “Asymptotic analysis of solving an inverse boundary value problem for a nonlinear singularly perturbed time-periodic reaction-diffusion-advection equation”, J. Inverse Ill-Posed Probl., 27:5 (2019), 745–758  crossref  mathscinet  zmath  isi  scopus
    20. E. Tabarintseva, “Approximate solving of an inverse problem for a parabolic equation with nonlocal data”, 2019 15Th International Asian School-Seminar Optimization Problems of Complex Systems (OPCS 2019), IEEE, 2019, 173–178  isi
    Citing articles in Google Scholar: Russian citations, English citations
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    Sibirskii Zhurnal Vychislitel'noi Matematiki
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