American Institute of Mathematical Sciences

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June  2007, 6(2): 487-503. doi: 10.3934/cpaa.2007.6.487

Blowup behaviors for degenerate parabolic equations coupled via nonlinear boundary flux

Chunlai Mu 1, and  Zhaoyin Xiang 2,

1. 

Department of Mathematics, Chongqing University, Chongqing 400044, China
2. 

School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu 610054, China

Received  June 2006 Revised  December 2006 Published  March 2007

This paper deals with the blow-up properties of solutions to a degenerate parabolic system coupled via nonlinear boundary flux. Firstly, we construct the self-similar supersolution and subsolution to obtain the critical global existence curve. Secondly, we establish the precise blow-up rate estimates for solutions which blow up in a finite time. Finally, we investigate the localization of blow-up points. The critical curve of Fujita type is conjectured with the aid of some new results.
Keywords: Degenerate parabolic system, critical global existence curve, critical Fujita curve, blow-up rate estimates, blow-up sets..
Mathematics Subject Classification: Primary: 35K55, 35K65, 35K60; Secondary: 35B33, 35B4.
Citation: Chunlai Mu, Zhaoyin Xiang. Blowup behaviors for degenerate parabolic equations coupled via nonlinear boundary flux. Communications on Pure and Applied Analysis, 2007, 6 (2) : 487-503. doi: 10.3934/cpaa.2007.6.487
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