The Enemy boundary value problem for a class of third-order equations

Abstract

The Vrag boundary value problem for a third-order equation of a mixed-compound type in a quadrilateral domain is considered. Using the Galerkin method under certain conditions for the coefficients and the right side of the equation, the existence of a weakly generalized solution in Sobolev space has been proved. Under the same conditions, the uniqueness of the generalized solution has been proved.