|
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
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
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
Linking options:
https://www.mathnet.ru/eng/chfmj280 https://www.mathnet.ru/eng/chfmj/v7/i2/p164
|
Statistics & downloads: |
Abstract page: | 212 | Full-text PDF : | 144 | References: | 43 |
|