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September  2006, 5(3): 435-446. doi: 10.3934/cpaa.2006.5.435

Blow-up and asymptotic behavior of solutions to a semilinear integrodifferential system

Qiong Chen 1, , Chunlai Mu 1, and  Zhaoyin Xiang 2,

1. 

Department of Mathematics, Sichuan University, Chengdu 610064, China
2. 

Department of Mathematics, China West Normal University, Nanchong 637002

Received  April 2005 Revised  September 2005 Published  June 2006

This paper deals with the blow-up properties and asymptotic behavior of solutions to a semilinear integrodifferential system with nonlocal reaction terms in space and time. The blow-up conditions are given by a variant of the eigenfunction method combined with new properties on systems of differential inequalities. At the same time, the blow-up set is obtained. For some special cases, the asymptotic behavior of the blow-up solution is precisely characterized.
Keywords: blow-up set, Integrodifferential system, asymptotic behavior., blow-up.
Mathematics Subject Classification: Primary: 35K57, 35B40; Secondary: 35K6.
Citation: Qiong Chen, Chunlai Mu, Zhaoyin Xiang. Blow-up and asymptotic behavior of solutions to a semilinear integrodifferential system. Communications on Pure and Applied Analysis, 2006, 5 (3) : 435-446. doi: 10.3934/cpaa.2006.5.435
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