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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2024, Number 3, Pages 38–49
DOI: https://doi.org/10.26907/0021-3446-2024-3-38-49
(Mi ivm9961)
 

Coefficient inverse problem for an equation of mixed parabolic-hyperbolic type with a non-characteristic line of type change

D. K. Durdiev

Bukhara branch of the Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan, Bukhara State University, 11 M.Ikbol str., Bukhara, 200100 Republic of Uzbekistan
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Abstract: In this paper, we study the direct and two inverse problems for a model equation of mixed parabolic-hyperbolic type. In the direct problem, the Tricomi problem for this equation with a non-characteristic line of type change is considered. The unknown of the inverse problem is the variable coefficient at the lowest derivative in the parabolic equation. To determine it, two inverse problems are studied: with respect to the solution defined in the parabolic part of the domain, the integral overdetermination condition (inverse problem 1) and one simple observation at a fixed point (inverse problem 2) are given. Theorems on the unique solvability of the formulated problems in the sense of classical solution are proved.
Keywords: inverse problem, mixed-type equation, characteristic, Green's function, contraction mapping principle.
Received: 09.02.2023
Revised: 27.03.2023
Accepted: 29.05.2023
Document Type: Article
UDC: 517.968
Language: Russian
Citation: D. K. Durdiev, “Coefficient inverse problem for an equation of mixed parabolic-hyperbolic type with a non-characteristic line of type change”, Izv. Vyssh. Uchebn. Zaved. Mat., 2024, no. 3, 38–49
Citation in format AMSBIB
\Bibitem{Dur24}
\by D.~K.~Durdiev
\paper Coefficient inverse problem for an equation of mixed parabolic-hyperbolic type with a non-characteristic line of type change
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2024
\issue 3
\pages 38--49
\mathnet{http://mi.mathnet.ru/ivm9961}
\crossref{https://doi.org/10.26907/0021-3446-2024-3-38-49}
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