Solving coefficient inverse problems for nonlinear singularly perturb e d equations of the reaction-diffusion-advection type with data on the position of a reaction front

被引：34

作者：

Lukyanenko, D. V. ^{[1
,2
]}

Borzunov, A. . A. . ^{[1
]}

Shishlenin, M. A. ^{[3
,4
,5
]}

机构：

[1] Lomonosov Moscow State Univ, Dept Math, Fac Phys, Moscow 119991, Russia

[2] Moscow Ctr Fundamental & Appl Math, Moscow 119234, Russia

[3] Inst Computat Math & Math Geophys SB RAS, Novosibirsk 630090, Russia

[4] Novosibirsk State Univ, Novosibirsk 630090, Russia

[5] Akademgorodok, Math Ctr, Novosibirsk 630090, Russia

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2021年 / 99卷

关键词：

Coefficient inverse problem; Reaction-diffusion-advection equation; Singularly perturbed problem; Inverse problem with data on the position of a reaction front; NUMERICAL-METHODS; CONTINUATION PROBLEM; BOUNDARY; MODEL; TERM;

D O I：

10.1016/j.cnsns.2021.105824

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An approach to solving coefficient inverse problems for nonlinear reaction-diffusionadvection equations is proposed. As an example, we consider an inverse problem of restoring a coefficient in a nonlinear Burgers-type equation. One of the features of the inverse problem is a use of additional information about the position of a reaction front. Another feature of the approach is a use of asymptotic analysis methods to select a good initial guess in a gradient method for minimizing a cost functional that occurs when solving the coefficient inverse problem. Numerical experiments demonstrate the effectiveness of the proposed approach. (c) 2021 Elsevier B.V. All rights reserved.

引用

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