Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Large-time behaviour of solutions to non-Newtonian filtration equations with nonlinear boundary sources

Zejia Wanga1, Jingxue Yina1 p1 and Chunpeng Wanga1

a1 Department of Mathematics, Jilin University, Changchun 130012, People's Republic of China (wangcp@jlu.edu.cn)

Abstract

This paper deals with the large-time behaviour of solutions to the exterior problem of the non-Newtonian filtration equation with first-order term and nonlinear boundary source. In particular, the critical global exponent and the critical Fujita exponent are determined or estimated. An interesting phenomenon is shown: there exists a threshold value for the coefficient of the first-order term such that the critical global exponent is strictly less than the critical Fujita exponent when the coefficient is under this threshold, while these two exponents are identically equal when the coefficient is over this value.

(Received April 15 2009)

(Accepted November 06 2009)

Correspondence:

p1 Present address: School of Mathematical Sciences, South China Normal University, Guangzhou 510631, People's Republic of China.