Some features of solving an inverse backward problem for a generalized Burgers’ equation-Reference-Cited by-同舟云学术

Some features of solving an inverse backward problem for a generalized Burgers’ equation

Published:2020-09-25 Issue:5 Volume:28 Page:641-649
ISSN:1569-3945
Container-title:Journal of Inverse and Ill-posed Problems
language:en
Short-container-title:

Author:

Lukyanenko Dmitry V.¹^ORCID,Prigorniy Igor V.²^ORCID,Shishlenin Maxim A.³

Affiliation:

1. Department of Mathematics, Faculty of Physics , Lomonosov Moscow State University , 119991; and Moscow Center of Fundamental and Applied Mathematics, 119234 Moscow , Russia

2. Department of Mathematics, Faculty of Physics , Lomonosov Moscow State University , 119991 Moscow , Russia

3. Novosibirsk State University ; and Sobolev Institute of Mathematics; and Institute of Computational Mathematics and Mathematical Geophysics, 630090 Novosibirsk , Russia

Abstract

Abstract In this paper, we consider an inverse backward problem for a nonlinear singularly perturbed parabolic equation of the Burgers’ type. We demonstrate how a method of asymptotic analysis of the direct problem allows developing a rather simple algorithm for solving the inverse problem in comparison with minimization of the cost functional. Numerical experiments demonstrate the effectiveness of this approach.

Funder

Russian Foundation for Basic Research

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/jiip-2020-0078/pdf

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