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
收藏
页码：93 / 106
页数：14
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