Boundary Value Problems
Volume 2008 (2008), Article ID 847145, 15 pages
Blowup for a Non-Newtonian Polytropic Filtration System Coupled via Nonlinear Boundary Flux
1Department of Mathematics, China West Normal University, Nanchong 637002, China
2College of Mathematics and Physics, Chongqing University, Chongqing 400044, China
3Department of Mathematics, Sichuan Normal University, Chengdu 610066, China
Received 18 November 2007; Accepted 1 March 2008
Academic Editor: Emmanuele DiBenedetto
Copyright © 2008 Zhongping Li 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.
We study the global existence and the global nonexistence of a non-Newtonian polytropic filtration system coupled via nonlinear boundary flux. We first establish a weak comparison principle, then discuss the large time behavior of solutions by using modified upper and lower solution methods and constructing various upper and lower solutions. Necessary and sufficient conditions on the global existence of all positive (weak) solutions are obtained.