Boundary Value Problem For One Class Of Third-Order Equations Of Mixed-Composite Type In A Quadrangular Region

Abstract

A boundary value problem for a third-order equation of mixed-composite type in a quadrangular domain is considered. Using the Galerkin method, under certain conditions on the coefficients and the right-hand side of the equation, the existence of a weakly generalized solution in the Sobolev space is proved. Under the same conditions, the uniqueness of the generalized solution is proved.