Glasgow Mathematical Journal

Research Article

GLOBAL EXISTENCE AND BLOW-UP FOR NON-NEWTON POLYTROPIC FILTRATION SYSTEM COUPLED WITH LOCAL SOURCE

JUN ZHOUa1 c1 and CHUNLAI MUa2

a1 School of Mathematics and Statistics, Southwest University, Chongqing 400715, P. R. China e-mail: zhoujun_math@hotmail.com.

a2 School of Mathematics and Physics, Chongqing University, Chongqing 400044, P. R. China

Abstract

This paper deals with the global existence and blow-up properties of the following non-Newton polytropic filtration system coupled with local source: ut − Δm,pu = avα, vt − Δn,qv = buβ. Under appropriate hypotheses, we prove that the solution either exists globally or blows up in finite time depending on the initial data and the relations between αβ and mn(p − 1)(q − 1).

(Received February 25 2007)

(Accepted July 01 2008)

2000 AMS Subject Classification

  • 35K50;
  • 35K55;
  • 35K65;
  • 35B33

Correspondence:

c1 Corresponding author.