Boundary Value Problems
Volume 2008 (2008), Article ID 847145, 15 pages
doi:10.1155/2008/847145
Blowup for a non-Newtonian polytropic filtration system coupled via nonlinear boundary flux
Zhongping Li1
, Chunlai Mu2
and Yuhuan Li3
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
Abstract
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.