On the solvability of an inverse problem for the Burgers equation with an integral overdetermination condition in a nonlinearly degenerating domain
Yergaliyev M.G. Jenaliyev M.T. Kabanikhin S.I. Kassen M.
1 February 2025Walter de Gruyter GmbH
Journal of Inverse and Ill-Posed Problems
2025#33Issue 193 - 106 pp.
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.
Burgers equation , integral overdetermination condition , Inverse problem , non-parabolic domain , periodic boundary condition
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Department of Differential Equations, Institute of Mathematics and Mathematical Modeling, al-Farabi KazNU, Almaty, Kazakhstan
Department of Mecnanics and Mathematics, al-Farabi KazNU, Almaty, Kazakhstan
Department of Differential Equations, Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russian Federation
Department of Differential Equations
Department of Mecnanics and Mathematics
Department of Differential Equations
Sobolev Institute of Mathematics SB RAS
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