On Solonnikov-Fasano Problem for the Burgers Equation

Abstract

The paper is devoted to the questions of solvability in the Sobolev classes for boundary value problem for the Burgers equation with boundary conditions of the Solonnikov-Fasano type in degenerating domain with degenerate point at the origin. By applying the Galerkin methods and a priori estimates we prove the Existence and Uniqueness Theorems for the solution of the considered boundary value problem, as well as its regularity with increasing smoothness of given functions.