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.

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