Solving of the coefficient inverse problem for a nonlinear singularly perturbed two-dimensional reaction-diffusion equation with the location of moving front data

被引：39

作者：

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

Grigorev, V. B. ^{[1
]}

Volkov, V. T. ^{[1
]}

Shishlenin, M. A. ^{[2
,3
,4
]}

机构：

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

[2] Sobolev Inst Math, Novosibirsk 630090, Russia

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

[4] Novosibirsk State Univ, Novosibirsk 630090, Russia

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2019年 / 77卷 / 05期

关键词：

Coefficient inverse problem; Singularly perturbed problem; Interior and boundary layers; Reaction-diffusion-advection equation; BOUNDARY CONTROL; RECONSTRUCTION; ALGORITHM; GELFAND; LEVITAN; KREIN;

D O I：

10.1016/j.camwa.2018.11.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Asymptotic-numerical approach to solving the coefficient inverse problem for a nonlinear singularly perturbed two-dimensional reaction-diffusion equation by knowing the location of moving front data is proposed. Asymptotic analysis of the direct problem allows to reduce the original two-dimensional parabolic problem to a series of more simple equations with lower dimension for the determination of moving front parameters. It enables to associate the observed location of the moving front to the parameters which have to be identified. Numerical examples show the effectiveness of the proposed method. (C) 2018 Elsevier Ltd. All rights reserved.

引用

页码：1245 / 1254

页数：10

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