Blow-up for nonlinear heat equations with absorptions

Abstract

This paper deals with the blow-up of positive solution of the nonlinear heat equation $u_t = bigtriangledown (a(u) bigtriangledown u)- f (u)$ subject to nonlinear boundary condition $frac{partial u}{partial n} = b (u)$ Under suitable assumptions on nonlinear functions a, $f$ , b and initial data $u_0$(x), we obtain the blow-up rate and the blow-up set of the solutions of the problem by the Nirenberg maximum principle.