This article is cited in 7 papers

Inverse Problem for an Integrodifferential Equation of the Hyperbolic Type protect in a Rectangular Domain

D. K. Durdiev^ab, J. Sh. Safarov<sup>ac

a</sup> V. I. Romanovskiy Institute of Mathematcs of the Academy of Sciences of Uzbekistan, Tashkent
^b Bukhara State University
^c Tashkent University of Information Technology

Abstract: The inverse problem of determining the solution and the kernel of the integral term in an inhomogeneous two-dimensional integrodifferential wave equation in a rectangular domain is considered. First, the uniqueness of the solution of the direct problem is established using the completeness of the eigenfunction system of the corresponding homogeneous Dirichlet problem for the two-dimensional Laplace operator, and the existence of a solution of the direct problem is proved. Using additional information about the solution of the direct problem, we obtain a Volterra integral equation of the second kind for the kernel of the integral term. The existence and uniqueness of a solution of this equation is proved by the contraction mapping method in the space of continuous functions with a weighted norm.

Keywords: integrodifferential equation, integral kernel, Fourier method, eigenfunctions, eigenvalues, Banach theorem.

UDC: 517.958

MSC: 35R30

Received: 10.08.2022
Revised: 06.01.2023

DOI: 10.4213/mzm13686

 English version: Mathematical Notes, 2023, 114:2, 199–211

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