Abstract:
We consider a model case of stationary vibrations of a thin flat plate, one side of which is embedded, the opposite side is free, and the sides are freely leaned. In mathematical modeling there is a local boundary value problem for the biharmonic equation in a rectangular domain. Boundary conditions are given on all boundary of the domain. We show that the considered problem is self-adjoint. Herewith the problem is ill-posed. We show that the stability of solution to the problem is disturbed. Necessary and sufficient conditions of existence of the problem solution are found. Spaces of the ill-posedness of the considered problem are constructed.
Citation:
U. A. Iskakova, “On a model of oscillations of a thin flat plate with a variety of mounts on opposite sides”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 9:2 (2016), 110–116
\Bibitem{Isk16}
\by U.~A.~Iskakova
\paper On a model of oscillations of a thin flat plate with a variety of mounts on opposite sides
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2016
\vol 9
\issue 2
\pages 110--116
\mathnet{http://mi.mathnet.ru/vyuru319}
\crossref{https://doi.org/10.14529/mmp160210}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000376997200010}
\elib{https://elibrary.ru/item.asp?id=26224828}
Citation in format AMSBIB
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