On the Features of Numerical Solution of Coefficient Inverse Problems for Nonlinear Equations of the Reaction–Diffusion–Advection Type with Data of Various Types

On the Features of Numerical Solution of Coefficient Inverse Problems for Nonlinear Equations of the Reaction–Diffusion–Advection Type with Data of Various Types Full article

Journal

Differential Equations
ISSN: 0012-2661 , E-ISSN: 1608-3083

Output data

Year: 2023, Volume: 59, Number: 12, Pages: 1734-1757 Pages count : 24 DOI: 10.1134/s0012266123120133

Authors

Lukyanenko D.V. ^1,2 , Argun Raul ¹ , Borzunov A.A. ¹ , Gorbachev A.V. ¹ , Shinkarev V.D. ¹ , Shishlenin Maxim A. ^3,4 , Yagola A.G. ¹

Affiliations

1	Lomonosov Moscow State University, Moscow, 119991, Russia
2	Moscow Center for Fundamental and Applied Mathematics
3	Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia
4	Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences

Funding (1)

Russian Science Foundation

23-11-00069

The paper discusses the features of constructing numerical schemes for solving coefficient inverse problems for nonlinear partial differential equations of the reaction–diffusion–advection type with data of various types. As input data for the inverse problem, we consider (1) data at the final moment of time, (2) data at the spatial boundary of a domain, (3) data at the position of the reaction front. To solve the inverse problem in all formulations, the gradient method of minimizing the target functional is used. In this case, when constructing numerical minimization schemes, both an approach based on discretization of the analytical expression for the gradient of the functional and an approach based on differentiating the discrete approximation of the functional to be minimized are considered. Features of the practical implementation of these approaches are demonstrated by the example of solving the inverse problem of reconstructing the linear gain coefficient in a nonlinear Burgers-type equation.

Lukyanenko D.V. , Argun R. , Borzunov A.A. , Gorbachev A.V. , Shinkarev V.D. , Shishlenin M.A. , Yagola A.G.
On the Features of Numerical Solution of Coefficient Inverse Problems for Nonlinear Equations of the Reaction–Diffusion–Advection Type with Data of Various Types
Differential Equations. 2023. V.59. N12. P.1734-1757. DOI: 10.1134/s0012266123120133 WOS Scopus РИНЦ OpenAlex

Submitted:	Sep 28, 2023
Accepted:	Nov 15, 2023
Published print:	Dec 27, 2023
Published online:	Feb 26, 2024

Web of science:	WOS:001172870000009
Scopus:	2-s2.0-85186451601
Elibrary:	65590236
OpenAlex:	W4392175627

DB	Citing
OpenAlex	4
Scopus	5
Web of science	5
Elibrary	4