American Institute of Mathematical Sciences

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December  2005, 4(4): 721-733. doi: 10.3934/cpaa.2005.4.721

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

Lili Du 1, , Chunlai Mu 2, and  Zhaoyin Xiang 3,

1. 

School of Mathematics Sciences, South China University of Technology, Guangzhou 510640,, China
2. 

Department of Mathematics, Sichuan University, Chengdu 610064, China
3. 

Department of Mathematics, China West Normal University, Nanchong 637002, China

Received  October 2004 Revised  May 2005 Published  September 2005

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: blow-up, reaction-diffusion system, nonlinear memory, Global existence.
Mathematics Subject Classification: Primary: 35B40, 35K57; Secondary: 35K60.
Citation: Lili Du, Chunlai Mu, Zhaoyin Xiang. Global existence and blow-up to a reaction-diffusion system with nonlinear memory. Communications on Pure & Applied Analysis, 2005, 4 (4) : 721-733. doi: 10.3934/cpaa.2005.4.721
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