Initial–Boundary Value Problems for Equation of Oscillations of a Rectangular Plate

In this paper, we study problems with initial conditions for equation of oscillations of a rectangular plate subject to various boundary conditions. We establish an energy inequality, which implies the uniqueness of solution to three initial-boundary value problems. In the case, when the plate is hi...

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Bibliographic Details
Published inRussian mathematics Vol. 65; no. 10; pp. 52 - 62
Main Author Sabitov, K. B.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.10.2021
Springer Nature B.V
Subjects
Boundary conditions
Boundary value problems
Existence theorems
Initial conditions
Mathematics
Mathematics and Statistics
Oscillations
Rectangular plates
initial–boundary value problem
uniqueness
series
existence
equation of oscillations of a rectangular plate
energy inequality
stability
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Summary:In this paper, we study problems with initial conditions for equation of oscillations of a rectangular plate subject to various boundary conditions. We establish an energy inequality, which implies the uniqueness of solution to three initial-boundary value problems. In the case, when the plate is hinged at its edges, we prove existence and stability theorems for the problem solution in classes of regular and generalized solutions.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X21100054