Singularity and Decay Estimates for a Degenerate Parabolic Equation

Abstract

In this paper, a degenerate parabolic equation ut−divxθ∇u=xaup with p>1 and θ<2,a∈ℝ, is considered. Based on rescaling arguments combined with a doubling property, the space-time singularity and decay estimates are established. Moreover, a universal and a priori bound of global nonnegative solutions for the corresponding initial boundary value problem is derived.