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

Qiong Chen; Chunlai Mu; Zhaoyin Xiang

doi:10.3934/cpaa.2006.5.435

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2006, Volume 5, Issue 3: 435-446. Doi: 10.3934/cpaa.2006.5.435

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

1.
Department of Mathematics, Sichuan University, Chengdu 610064
2.
Department of Mathematics, China West Normal University, Nanchong 637002

Received: March 31, 2005

Revised: August 31, 2005

Published: August 2006

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Abstract

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.

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Mathematics Subject Classification: Primary: 35K57, 35B40; Secondary: 35K60.

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

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