Статья

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

J. Sh. SafarovDiplomat University, 1, Sayilgoh stS., Tashkent 100047, UzbekistanАскар Ахмадович РахмоновBukhara State University, 11, M.Ikbol str., Bukhara 200114, UzbekistanMaftunakhon SafarovaTashkent University of Information Technologies, Amir Timur str., 108, Tashkent 100202, Uzbekistan

AIP conference proceedingsjournal2024en

ABI

Аннотация

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.

Темы

Differential Equations and Boundary Problems Stability and Controllability of Differential Equations Differential Equations and Numerical Methods

Идентификаторы

DOI: 10.1063/5.0201252

Цитирования и источники

Цитирований: 0Использованных источников: 16

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