Boundary Value Problems
Volume 2011 (2011), Article ID 750769, 18 pages
doi:10.1155/2011/750769
Research Article

A Quasilinear Parabolic System with Nonlocal Boundary Condition

Botao Chen,1 Yongsheng Mi,1,2 and Chunlai Mu2

1College of Mathematics and Computer Sciences, Yangtze Normal University, Fuling, Chongqing 408100, China
2College of Mathematics and Physics, Chongqing University, Chongqing 401331, China

Received 8 May 2010; Revised 25 July 2010; Accepted 11 August 2010

Academic Editor: Daniel Franco

Copyright © 2011 Botao Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate the blow-up properties of the positive solutions to a quasilinear parabolic system with nonlocal boundary condition. We first give the criteria for finite time blowup or global existence, which shows the important influence of nonlocal boundary. And then we establish the precise blow-up rate estimate. These extend the resent results of Wang et al. (2009), which considered the special case m1=m2=1, p1=0, q2=0, and Wang et al. (2007), which studied the single equation.