THE ESTIMATION OF SOLUTIONS NONDIVERGENT ELLIPTIC-PARABOLIC EQUATIONS

Abstract

The degenerate elliptic-parabolic equations arise as mathematical models of various applied problems of mechanics, for instance in reaction drift diffusion processes of electrically charged species phase transition processes and transport processes in porous media. Investigations of boundary value problems for second order degenerate elliptic-parabolic equations ascend to the work by Keldysh [1], where correct statements for boundary value problems were considered for the case of one space variable as well as existence and uniqueness of solutions. In the work by Fichera [2] boundary value problems were given for multidimentional case. He proved existence of generalized solutions to these boundary value problems. Let Ω be a bounded open set in R and QT = Ω × (0, T ) , T > 0 be a cylinder. We consider the following initial boundary value problem