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

  • Dmitry V. Lukyanenko ORCID logo EMAIL logo , Igor V. Prigorniy ORCID logo and Maxim A. Shishlenin

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.

MSC 2010: 35R30; 65M32

Dedicated to Professor Anatoly Yagola on the occasion of his 75th birthday


Award Identifier / Grant number: 18-01-00865

Award Identifier / Grant number: 19-01-00694

Funding statement: This work was supported by RFBR (projects no. 18-01-00865 and 19-01-00694).

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Received: 2020-06-30
Revised: 2020-08-26
Accepted: 2020-08-30
Published Online: 2020-09-25
Published in Print: 2020-11-01

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