Abstract
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.
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ACKNOWLEDGMENTS
The author is grateful to Professor M.M. Karchevskii, since this work was performed on his advice after our conversation with him at a conference organized by Kazan Federal University on September 7–12, 2019.
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Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 10, pp. 60–70.
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Sabitov, K.B. Initial–Boundary Value Problems for Equation of Oscillations of a Rectangular Plate. Russ Math. 65, 52–62 (2021). https://doi.org/10.3103/S1066369X21100054
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DOI: https://doi.org/10.3103/S1066369X21100054