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

被引：0

作者：

Jenaliyev, Muvasharkhan T. ^{[1
]}

Kabanikhin, Sergey I. ^{[3
]}

Kassen, Medina ^{[2
,4
]}

Yergaliyev, Madi G. ^{[1
,2
]}

机构：

[1] Inst Math & Math Modeling, Dept Differential Equat, Alma Ata, Kazakhstan

[2] al Farabi KazNU, Dept Mecnan & Math, Alma Ata, Kazakhstan

[3] RAS, SB, Sobolev Inst Math, Novosibirsk, Russia

[4] KazNU al Farabi, Karagandy 100026, Kazakhstan

来源：

JOURNAL OF INVERSE AND ILL-POSED PROBLEMS | 2025年 / 33卷 / 01期

关键词：

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

D O I：

10.1515/jiip-2024-0067

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：93 / 106

页数：14

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