Numerical and mathematical approach to the support splitting phenomena for some nonlinear diffusion equations(Theory, Scientific Computation and Numerical Analysis, Special Issue on "Joint Symposium of JSIAM Activity Groups 2007")

Abstract

We consider support splitting phenomena for the porous media equation with the interaction between diffusion and absorption, which describes the flow through the absorbing medium. Here the support means the region occupied by the fluid. In the 1-dimensional case, using the L^1, L^∞ estimates, we have some sufficient conditions under which the support begins to split. In this paper we justify these sufficient conditions from the view point of particular solutions. The extension of the present method to multidimensional problems can be expected.