On Solonnikov-Fasano Problem for the Burgers Equation

On Solonnikov-Fasano Problem for the Burgers Equation

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The paper is devoted to the questions of solvability in the Sobolev classes for boundary value Collections 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 Glutathione well as its regularity with increasing smoothness of given functions.