Behaviour of the support of the solution appearing in some nonlinear diffusion equation with absorption

Abstract

Numerical experiments suggest interesting properties in the several fields of fluid dynamics, plasma physics and population dynamics.  Among such properties, we may observe the interesting phenomena; that is, the repeated appearance and disappearance phenomena of the region penetrated by the fluid in the flow through a porous media with absorption. The model equation in two dimensional space is written in the form of the initial-boundary value problem for a nonlinear diffusion equation with the effect of absorption.
In this paper we show some numerical examples and prove such phenomena.