Geodesic
On a model of oscillations of a thin flat plate with a variety of mounts on opposite sides
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 9 (2016) no. 2, pp. 110-116

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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.
Keywords: oscillations; thin flat plate; biharmonic equation; boundary value problem; ill-posed problem. 
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     author = {U. A. Iskakova},
     title = {On a model of oscillations of a thin flat plate with a variety of mounts on opposite sides},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {110--116},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2016_9_2_a9/}
}
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U. A. Iskakova. On a model of oscillations of a thin flat plate with a variety of mounts on opposite sides. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 9 (2016) no. 2, pp. 110-116. http://geodesic.mathdoc.fr/item/VYURU_2016_9_2_a9/