Singularity and Decay Estimates for a Degenerate Parabolic Equation. (11th March 2021) - Li, Dongyan
Abstract : In this paper, a degenerate parabolic equation u t − div x θ ∇ u = x a u p 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.