Parabolic Equations with a Singular Absorption: Extinction Versus Blow-up

Abstract

We prove a local existence of weak solutions of semilinear parabolic equations with a strong singular absorption and a source. Moreover, we consider the qualitative behavior of solutions. We show that any solution exists globally and vanishes after a finite time if either the initial data or the source term is small enough. On the other hand, we point out some criteria such that solutions are explosive in a finite time. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.