Blow-up phenomena for some nonlinear parabolic problems

Abstract

We consider the blow-up of solutions of equations of the form ut = div (ρ (| ∇ u |2) grad u) + f (u) by means of a differential inequality technique. A lower bound for blow-up time is determined if blow-up does occur as well as a criterion for blow-up and conditions which ensure that blow-up cannot occur. © 2007 Elsevier Ltd. All rights reserved.