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

Izv. Vyssh. Uchebn. Zaved. Mat., 2021 Number 10, Pages 60–70 (Mi ivm9721)

This article is cited in 10 papers

Initial-boundary value problems for equation of oscillation of a rectangular plate

K. B. Sabitovab

a Sterlitamak Branch of the Institute for Strategic Studies of the Republic of Bashkortostan, 68 Odesskaya str., Sterlitamak, 453103 Russia
b Samara State Technical University, 244 Molodogvardeyskaya str., Samara, 443100, Russia

Abstract: The paper investigates problems with initial conditions for the equation of vibrations of a rectangular plate with different boundary conditions. An energy inequality is established, which implies the uniqueness of the solution of the three initial-boundary value problems. In the case of a hinged plate at the edges, 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 problems, energy inequality, uniqueness, series, existence, stability.

UDC: 517.95: 624.04

Received: 16.11.2020
Revised: 16.11.2020
Accepted: 24.12.2020

DOI: 10.26907/0021-3446-2021-10-60-70


 English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2021, 65:10, 52–62


© Steklov Math. Inst. of RAS, 2025