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Chelyabinskiy Fiziko-Matematicheskiy Zhurnal, 2022, Volume 7, Issue 2, Pages 164–180
DOI: https://doi.org/10.47475/2500-0101-2022-17203
(Mi chfmj280)
 

Mathematics

On some class of the pseudohyperbolic equations with an unknown coefficient

A. I. Kozhanova, R. R. Safiullovab

a Sobolev Institute of Mathematics of Siberian Branch of RAS, Novosibirsk, Russia
b Ufa State Aviation Technical University, Ufa, Russia
References:
Abstract: We consider the inverse problems with an unknown coefficient $a$ for a pseudohyperbolic equation $u_{tt}-\Delta u-\Delta u_{tt}+au=f(x,t)$ and investigate the solvability of the problem. We prove the theorems of the existence of the problem's regular solutions. The distinctiveness of the problems is a presence of new overdetermination conditions for the considered class of equations.
Keywords: pseudohyperbolic equation, unknown coefficient, inverse problem, integral overdetermination, regular solution, existence.
Received: 13.03.2022
Revised: 14.04.2022
Bibliographic databases:
Document Type: Article
UDC: 517.956
Language: Russian
Citation: A. I. Kozhanov, R. R. Safiullova, “On some class of the pseudohyperbolic equations with an unknown coefficient”, Chelyab. Fiz.-Mat. Zh., 7:2 (2022), 164–180
Citation in format AMSBIB
\Bibitem{KozSaf22}
\by A.~I.~Kozhanov, R.~R.~Safiullova
\paper On some class of the pseudohyperbolic equations with an unknown coefficient
\jour Chelyab. Fiz.-Mat. Zh.
\yr 2022
\vol 7
\issue 2
\pages 164--180
\mathnet{http://mi.mathnet.ru/chfmj280}
\crossref{https://doi.org/10.47475/2500-0101-2022-17203}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4460043}
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