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= ∇ (a(u) ∇u)-f(u) subject to nonlinear boundary condition ∂u / ∂n = b(u). Under suitable assumptions on nonlinear functions a, f, b and initial data u_o, we obtain the blow-up rate and the blow-up set of the solutions of the problem by the Nirenberg maximum principle.