On one Ill-posed Problem for a Biharmonic Equation

Abstract

A local boundary value problem for the biharmonic equation in a
rectangular domain is considered. 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.