Asymptotic stability and blow-up of solutions for semi-linear edge-degenerate parabolic equations with singular potentials

Abstract

This article studies the initial boundary value problem for a class of semilinear edge-degenerate parabolic equations with singular potential term. By introducing a family of potential wells, we derive a threshold of the existence of global solutions with exponential decay, and the blow-up in finite time in both cases with low initial energy and critical initial energy.