SOLVABILITY OF THE INVERSE PROBLEM FOR THE PSEUDOHYPERBOLIC EQUATION

Aitzhanov S.E. Ferreira J. Zhalgassova K.A.
2022 al-Farabi Kazakh State National University

KazNU Bulletin. Mathematics, Mechanics, Computer Science Series
2022 #115 Issue 3 3 - 15 pp.

This paper investigates the solvability of the inverse problem of finding a solution and an unknown coefficient in a pseudohyperbolic equation known as the Klein-Gordon equation. A distinctive feature of the given problem is that the unknown coefficient is a function that depends only on the time variable. The problem is considered in the cylinder, the conditions of the usual initial-boundary value problem are set. The integral overdetermination condition is used as an additional condition. In this paper, the inverse problem is reduced to an equivalent problem for the loaded nonlinear pseudohyperbolic equation. Such equations belong to the class of partial differential equations, not resolved with respect to the highest time derivative, and they are also called composite type equations. The proof uses the Galerkin method and the compactness method (using the obtained a priori estimates). For the problem under study, the authors prove existence and uniqueness theorems for the solution in appropriate classes.

compactness method , existence , Galerkin method , inverse problem , Klein-Gordon equation , Pseudohyperbolic equation , uniqueness

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Al-Farabi Kazakh National University, Almaty, Kazakhstan
Federal University of Fluminense, Volta Redonda, Brazil
M.Auezov South Kazakhstan University, Shymkent, Kazakhstan

Al-Farabi Kazakh National University
Federal University of Fluminense
M.Auezov South Kazakhstan University

10 лет помогаем публиковать статьи Международный издатель

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