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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2022, Volume 62, Number 3, Pages 451–461
DOI: https://doi.org/10.31857/S0044466922030024 (Mi zvmmf11374) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Mathematical physics

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

R. L. Arguna, A. V. Gorbacheva, D. V. Lukyanenkoab, M. A. Shishlenincd

a Faculty of Physics, Lomonosov Moscow State University
b Moscow Center for Fundamental and Applied Mathematics, Lomonosov Moscow State University, 119234, Moscow, Russia
c Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia
d Novosibirsk State University, 630090, Novosibirsk, Russia
Citations (2)
DOI: https://doi.org/10.31857/S0044466922030024
Abstract: A new approach to the reconstruction of a boundary condition in an inverse problem for a nonlinear singularly perturbed reaction–diffusion–advection equation with data on the reaction front position is proposed. The problem is solved via gradient minimization of a cost functional with an initial approximation chosen by applying asymptotic analysis methods. The efficiency of the proposed approach is demonstrated by numerical experiments.
Key words: inverse problem with data on the position of a reaction front, inverse boundary value problem, reaction–diffusion–advection equation.
Funding agency Grant number
Russian Foundation for Basic Research 20-31-70016
This work was supported by the Russian Foundation for Basic Research, project no. 20-31-70016.
Received: 31.03.2021
Revised: 08.04.2021
Accepted: 20.05.2021
English version:
Computational Mathematics and Mathematical Physics, 2022, Volume 62, Issue 3, Pages 441–451
DOI: https://doi.org/10.1134/S0965542522030022
Bibliographic databases:
Document Type: Article
UDC: 519.6
Language: Russian
Citation: 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”, Zh. Vychisl. Mat. Mat. Fiz., 62:3 (2022), 451–461; Comput. Math. Math. Phys., 62:3 (2022), 441–451
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/zvmmf/v62/i3/p451
    • This publication is cited in the following 2 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. 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
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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