Blow-up for nonlinear heat equations with absorptions

Authors

  • Hailiang Zhang
  • Xiulan Guo

Keywords:

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

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.

 

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Published

2008-09-18

Issue

Section

Partial Differential Equations and Dynamical Systems

How to Cite

Blow-up for nonlinear heat equations with absorptions. (2008). European Journal of Pure and Applied Mathematics, 1(3), 33-39. https://www.ejpam.com/index.php/ejpam/article/view/93