Geodesic
Initial-boundary value problems for equation of oscillation of a rectangular plate
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2021), pp. 60-70

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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, stability.
Mots-clés : existence 
@article{IVM_2021_10_a4,
     author = {K. B. Sabitov},
     title = {Initial-boundary value problems for equation of oscillation of a rectangular plate},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {60--70},
     publisher = {mathdoc},
     number = {10},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_10_a4/}
}
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K. B. Sabitov. Initial-boundary value problems for equation of oscillation of a rectangular plate. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2021), pp. 60-70. http://geodesic.mathdoc.fr/item/IVM_2021_10_a4/