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JOURNALS // Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika // Archive

Izv. Vyssh. Uchebn. Zaved. Mat., 2023 Number 3, Pages 63–77 (Mi ivm9862)

Plate oscillations with mixed boundary conditions

K. B. Sabitovab

a Institute of Mathematics with Computing Centre Ufa Federal Research Centre of the Russian Academy of Sciences, 112 Chernyshevsky str., Ufa, 450008 Russia
b Sterlitamak branch of the Ufa University of Science and Technology, 49 Lenina Ave., Sterlitamak, 453103 Russia

Abstract: In this paper problem with initial conditions for the equation of vibrations of a rectangular plate with boundary conditions is investigated. An energy inequality is established, which implies the uniqueness of the solution of the initial-boundary value problem. Existence and stability theorems for the solution of the problem in the classes of regular and generalized solutions are proved.

Keywords: equation of vibrations of a rectangular plate, initial boundary value problem, energy inequality, uniqueness, series, existence, stability.

UDC: 517.95

Received: 18.05.2022
Revised: 30.06.2022
Accepted: 28.09.2022

DOI: 10.26907/0021-3446-2023-3-63-77



© Steklov Math. Inst. of RAS, 2025