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

Lili Du; Chunlai Mu; Zhaoyin Xiang

doi:10.3934/cpaa.2005.4.721

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2005, Volume 4, Issue 4: 721-733. Doi: 10.3934/cpaa.2005.4.721

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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,
2.
Department of Mathematics, Sichuan University, Chengdu 610064
3.
Department of Mathematics, China West Normal University, Nanchong 637002

Received: September 30, 2004

Revised: April 30, 2005

Published: November 2005

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Abstract

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.

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

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