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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2023, Number 3, Pages 63–77
DOI: https://doi.org/10.26907/0021-3446-2023-3-63-77 (Mi ivm9862) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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
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DOI: https://doi.org/10.26907/0021-3446-2023-3-63-77
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.
Received: 18.05.2022
Revised: 30.06.2022
Accepted: 28.09.2022
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2023, Volume 67, Issue 3, Pages 53–65
DOI: https://doi.org/10.3103/S1066369X23030040
Document Type: Article
UDC: 517.95
Language: Russian
Citation: K. B. Sabitov, “Plate oscillations with mixed boundary conditions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 3, 63–77; Russian Math. (Iz. VUZ), 67:3 (2023), 53–65
Citation in format AMSBIB
\Bibitem{Sab23}
\by K.~B.~Sabitov
\paper Plate oscillations with mixed boundary conditions
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2023
\issue 3
\pages 63--77
\mathnet{http://mi.mathnet.ru/ivm9862}
\crossref{https://doi.org/10.26907/0021-3446-2023-3-63-77}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2023
\vol 67
\issue 3
\pages 53--65
\crossref{https://doi.org/10.3103/S1066369X23030040}
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
     
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