ANZIAM  J.  48 (2006), 37-56

Blowup properties for several diffusion systems with localised sources

Zhaoyin Xiang   Department of Mathematics   Sichuan University   Chengdu   Sichuan 610064   P. R. China   zhaoyin-xiang@sohu.com Qiong Chen   Department of Mathematics   Sichuan University   Chengdu   Sichuan 610064   P. R. China   and Chunlai Mu   Department of Mathematics   Sichuan University   Chengdu   Sichuan 610064   P. R. China

Abstract

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.

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