Large Time Behavior of a Nonlinear Diffusion Equation with a Source

Abstract

In this paper we study the positive solutions of the nonlinear diffusion equation u_t - Δu^m = u^{-p} in R^N in the class of functions with some prescribed growth rate as |x| → ∞. We give a description of the large time behavior and show that it is determined by the competition between the diffusion and the source.