Blowup behaviors for degenerate parabolic equations coupled via nonlinear boundary flux

Chunlai Mu; Zhaoyin Xiang

doi:10.3934/cpaa.2007.6.487

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2007, Volume 6, Issue 2: 487-503. Doi: 10.3934/cpaa.2007.6.487

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Blowup behaviors for degenerate parabolic equations coupled via nonlinear boundary flux

Chunlai Mu¹ and
Zhaoyin Xiang^2,

1.
Department of Mathematics, Chongqing University, Chongqing 400044
2.
School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu 610054

Received: June 2006

Revised: December 2006

Published: June 2007

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Abstract

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.

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Mathematics Subject Classification: Primary: 35K55, 35K65, 35K60; Secondary: 35B33, 35B40.

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