L. N. Bondar', G. V. Demidenko, V. S. Nurmakhmatov, “Boundary value problem in a cylinder for a pseudohyperbolic equation”, Chelyab. Fiz.-Mat. Zh., 2023, Volume 8, Issue 4,Pages <nobr>469

This article is cited in 1 paper

Mathematics

Boundary value problem in a cylinder for a pseudohyperbolic equation

L. N. Bondar'^ab, G. V. Demidenko^ab, V. S. Nurmakhmatov^b

^a Sobolev Institute of Mathematics, Novosibirsk, Russia
^b Novosibirsk State University, Novosibirsk, Russia

Abstract: The paper considers the first boundary value problem in a cylinder for a pseudohyperbolic equation with variable coefficients. A theorem on the existence of a unique generalized solution of a boundary value problem in a Sobolev space is proved. Estimates for the solution are obtained.

Keywords: generalized solution, pseudohyperbolic equation, Sobolev spaces, Galerkin method.

UDC: 517.922

Received: 15.08.2023
Revised: 24.09.2023

DOI: 10.47475/2500-0101-2023-8-4-469-482