# American Institute of Mathematical Sciences

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

 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.
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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