Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

On the Critical Fujita Exponent for a Degenerate Parabolic System Coupled Via Nonlinear Boundary Flux

Jun Zhoua1 p1 and Chunlai Mua2 p2

a1 School of Mathematics and Statistics, Southwest University, Chongqing 400715, People's Republic of China

a2 College of Mathematics and Physics, Chongqing University, Chongqing 400044, People's Republic of China

Abstract

In this paper, we deal with the non-negative solutions of a degenerate parabolic system with nonlinear coupled boundary conditions and non-negative non-trivial compactly supported initial data. The critical Fujita exponents are given and the blow-up rates of the non-global solution are obtained.

(Received November 10 2005)

Keywords

  • Fujita exponents;
  • degenerate parabolic equations;
  • nonlinear boundary flux;
  • non-global solutions;
  • blow-up rate

Correspondence:

p1 Present address: Department of Mathematics, China West Normal University, Nanchong 637002, People's Republic of China (zhoujun_math@hotmail.com).

p2 Present address: Department of Mathematics, Sichuan University, Chengdu 610064, People's Republic of China.