Global existence and blow-up to a reaction-diffusion system with nonlinear memory

Pages: 721 - 733, Volume 4, Issue 4, December 2005

doi:10.3934/cpaa.2005.4.721       Abstract        Full Text (214.7K)       Related Articles

Lili Du - School of Mathematics Sciences, South China University of Technology, Guangzhou 510640,, China (email)
Chunlai Mu - Department of Mathematics, Sichuan University, Chengdu 610064, China (email)
Zhaoyin Xiang - Department of Mathematics, China West Normal University, Nanchong 637002, China (email)

Abstract: In this paper, we consider a reaction-diffusion system coupled by nonlinear memory. Under appropriate hypotheses, we prove that the solution either exists globally or blows up in finite time. Furthermore, the blow-up rate estimates are obtained.

Keywords:  Global existence, blow-up, reaction-diffusion system, nonlinear memory
Mathematics Subject Classification:  Primary: 35B40, 35K57; Secondary: 35K60

Received: October 2004;      Revised: May 2005;      Published: September 2005.