This article is cited in 1 paper

Differential Equations and Mathematical Physics

A criterion for the unique solvability of the spectral Dirichlet problem for a class of multidimensional hyperbolic-parabolic equations

S. A. Aldashev

Kazakh National Pedagogical University named after Abay, Almaty, 480100, Kazakhstan

Abstract: In the cylindrical domain of Euclidean space for one class of multidimensional hyperbolic parabolic equations the spectral Dirichlet problem with homogeneous boundary conditions is considered. The solution is sought in the form of an expansion in multidimensional spherical functions. The existence and uniqueness theorems of the solution are proved. Conditions for the unique solvability of the problem are obtained, which essentially depend on the height of the cylinder.

Keywords: multidimensional hyperbolic-parabolic equation, Dirichlet spectral problem, multidimensional cylindrical domain.

UDC: 517.955.2:517.956

MSC: 35M12, 35A02

Received: December 5, 2017
Revised: April 8, 2018
Accepted: June 11, 2018
First online: July 1, 2018

DOI: 10.14498/vsgtu1585

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