Application of the Fourier method to the study of a hyperbolic integro-differential equation in a rectangular domain

In the paper we investigate the solvability of the initial-boundary value problem for a nonhomogeneous integro-differential wave equation in a rectangular domain, when the integral kernel of the integral term is a known function. First, the uniqueness of the solution of the direct problem is establi...

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Bibliographic Details
Main Authors: Safarov, Jurabek, Rakhmonov, Askar, Safarova, Maftunakhon
Format: Conference Proceeding
Language:English
Subjects:
Boundary value problems
Differential equations
Dirichlet problem
Eigenvectors
Operators (mathematics)
Wave equations
Online Access:Get full text
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Summary:In the paper we investigate the solvability of the initial-boundary value problem for a nonhomogeneous integro-differential wave equation in a rectangular domain, when the integral kernel of the integral term is a known function. First, the uniqueness of the solution of the direct problem is established using the completeness property of the system of eigenfunctions of the corresponding homogeneous Dirichlet problem for the Laplace operator, further the existence of a solution to the direct problem is proved.
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0201252