Reaction–diffusion system approximation to degenerate parabolic systems

Abstract

In this paper, a degenerate parabolic system including Stefan and porous medium type systems is considered. We propose a reaction–diffusion system with a solution that approximates that of a degenerate parabolic system. The reaction–diffusion system includes only a simple reaction and linear diffusion. Resolving semi-linear problems is typically easier than dealing with nonlinear diffusion problems. Therefore, our ideas are expected to reveal new and more effective approaches to the study of nonlinear diffusion problems.