On the solvability of an inverse problem for the Burgers equation with an integral overdetermination condition in a nonlinearly degenerating domain

On the solvability of an inverse problem for the Burgers equation with an integral overdetermination condition in a nonlinearly degenerating domain Full article

Journal

Journal of Inverse and Ill-Posed Problems
ISSN: 0928-0219 , E-ISSN: 1569-3945

Output data

Year: 2025, Volume: 33, Number: 1, Pages: 24-41 Pages count : 18 DOI: 10.1515/jiip-2024-0067

Tags

Inverse problem; Burgers equation; non-parabolic domain; periodic boundary condition; integral overdetermination condition

Authors

Jenaliyev Muvasharkhan T. ¹ , Kabanikhin Sergey I. ² , Kassen Medina ³ , Yergaliyev Madi G. ^4,5

Affiliations

1	Department of Differential Equations , 374528 Institute of Mathematics and Mathematical Modeling , Almaty , Kazakhstan
2	Sobolev Institute of Mathematics SB RAS , Novosibirsk , Russia
3	Department of Mecnanics and Mathematics , al-Farabi KazNU , Almaty , Kazakhstan
4	Department of Differential Equations , 374528 Institute of Mathematics and Mathematical Modeling ; and Department of Mecnanics and Mathematics, al-Farabi KazNU , Almaty , Kazakhstan
5	Department of Differential Equations, Institute of Mathematics and Mathematical Modeling

The paper considers an inverse problem and a direct problem for the Burgers equation in a domain with movable boundaries. With the help of an additional condition, a formula is obtained for determining the desired function from a direct problem for the loaded Burgers equation for the solvability of which we require a condition on the functions according to which the boundaries of the domain change. The solvability of direct problems is proved using a priori estimates and the methods of Faedo–Galerkin and functional analysis.

Jenaliyev M.T. , Kabanikhin S.I. , Kassen M. , Yergaliyev M.G.
On the solvability of an inverse problem for the Burgers equation with an integral overdetermination condition in a nonlinearly degenerating domain
Journal of Inverse and Ill-Posed Problems. 2025. V.33. N1. P.24-41. DOI: 10.1515/jiip-2024-0067 WOS Scopus РИНЦ OpenAlex

Submitted:	Sep 26, 2024
Accepted:	Dec 15, 2024
Published online:	Jan 13, 2025
Published print:	Feb 1, 2025

Web of science:	WOS:001394844600001
Scopus:	2-s2.0-85215972348
Elibrary:	81302482
OpenAlex:	W4406295272

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