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Blowup properties for several diffusion systems with localised sources

Published online by Cambridge University Press:  17 February 2009

Zhaoyin Xiang ,
Qiong Chen  and
Chunlai Mu
Zhaoyin Xiang
Affiliation:
School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu 610054, P. R., China; e-mail: zhaoyin-xiang@sohu.com. Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R., China.
Qiong Chen
Affiliation:
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R., China.
Chunlai Mu
Affiliation:
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R., China.
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Abstract

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This paper investigates the Cauchy problem for two classes of parabolic systems with localised sources. We first give the blowup criterion, and then deal with the possibilities of simultaneous blowup or non-simultaneous blowup under some suitable assumptions. Moreover, when simultaneous blowup occurs, we also establish precise blowup rate estimates. Finally, using similar ideas and methods, we shall consider several nonlocal problems with homogeneous Neumann boundary conditions.

Keywords

diffusion systemlocalised sourceCauchy problemsimultaneous blowupblowup estimates.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 48 , Issue 1 , July 2006 , pp. 37 - 56
Copyright
Copyright © Australian Mathematical Society 2006

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