Application of the Fourier method to the study of a hyperbolic integro-differential equation in a rectangular domain
Journal: AIP conference proceedings
Year: 2024

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 prob