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November  2003, 9(6): 1519-1532. doi: 10.3934/dcds.2003.9.1519

Global existence and blow-up of solutions to a nonlocal reaction-diffusion system

Shu-Xiang Huang 1, , Fu-Cai Li 2, and  Chun-Hong Xie 2,

1. 

School of Mathematics and System Sciences, Shandong University, Jinan 250100, China
2. 

Department of Mathematics, Nanjing University, Nanjing 210093, China, China

Received  July 2002 Revised  May 2003 Published  September 2003

This paper deals with a reaction-diffusion system with nonlocal sources. Under appropriate hypotheses, we obtain that the solution either exists globally or blows up in finite time by making use of super and sub solution techniques. In the situation when the solution blows up in finite time, we show that the blow-up set is the whole domain, which is quite different from the results with local sources. Furthermore, we obtain the blow-up rate of the solution.
Keywords: global existence, Nonlocal reaction-diffusion system, blow-up set, blow-up rate., blow-up.
Mathematics Subject Classification: 35B40, 35K57, 35K6.
Citation: Shu-Xiang Huang, Fu-Cai Li, Chun-Hong Xie. Global existence and blow-up of solutions to a nonlocal reaction-diffusion system. Discrete & Continuous Dynamical Systems, 2003, 9 (6) : 1519-1532. doi: 10.3934/dcds.2003.9.1519
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