Abstract
We consider a model case of stationary vibrations of a thin at 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 sucient conditions of existence of the problem solution are found.Spaces of the ill-posedness of the considered problem are constructed.