An Initial-Boundary Value Problem for a Strongly Degenerate Higher-Order Even Equation

Abstract

In the present paper we investigate an initial-boundary value problem for a degenerate partial differential equation of high even order, in which the differential expression with respect to the spatial variable carries paired (linked) boundary data given simultaneously at both endpoints of the interval in a rectangular domain. Employing the Fourier method, the problem is reduced to an associated spectral problem, whose Green's function is constructed in closed form and shown to be symmetric by establishing the self-adjointness of the corresponding operator. On the basis of the eigenfunction expansion, the existence, uniqueness and continuous dependence of the solution on the given data are proved.