Singularity and blow-up estimates via Liouville-type theorems for Hardy-Hénon parabolic equations

Abstract

We consider the Hardy-Hénon parabolic equation $u_t-\Delta u=|x{|}^a|u{|}^{p-1}u$ with $p>1$ and $a\in \mathbb{R}$. We establish the space-time singularity and decay estimates, and Liouville-type theorems for radial and nonradial solutions. As applications, we study universal and a priori bound of global solutions as well as the blow-up estimates for the corresponding initial boundary value problem.