L. N. Bondar, V. Nurmakhmatov, “On solvability of the boundary value problem for one pseudohyperbolic equation”, Sib. Èlektron. Mat. Izv., 2021, Volume 18, Issue 2,Pages <nobr>1046

This article is cited in 2 papers

Differentical equations, dynamical systems and optimal control

On solvability of the boundary value problem for one pseudohyperbolic equation

L. N. Bondar^a, V. Nurmakhmatov^b

^a Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
^b Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia

Abstract: The paper considers the first boundary value problem in a rectangle for the equation describing torsional vibrations of an elastic rod. Existence and uniqueness theorems are proved for a generalized solution of the first boundary value problem in Sobolev space.

Keywords: generalized solution, pseudohyperbolic equation, torsional vibrations, Sobolev space, unique solvability, Galerkin method.

UDC: 517.922

MSC: 35E15

Received June 15, 2021, published October 19, 2021

Language: English

DOI: 10.33048/semi.2021.18.080