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

Muvasharkhan Jenaliyev, Sergey Igorevich Kabanikhin, Medina Kassen, Madi Yergaliyev

2025

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DOI 10.1515/jiip-2024-0067
Data confidence 70 medium
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Abstract

Abstract 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.