Blow-up for nonlinear heat equations with absorptions

Hailiang Zhang, Xiulan Guo

Abstract

This paper deals with the blow-up of positive solution of the nonlinear heat equation ut= ∇ (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 uo, we obtain the blow-up rate and the blow-up set of the solutions of the problem by the Nirenberg maximum principle.

 

Keywords

nonlinear heat equation; nonlinear boundary condition;blow-up; absorption; maximum principle.

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