International Journal of Differential Equations
Volume 2011 (2011), Article ID 896427, 9 pages
http://dx.doi.org/10.1155/2011/896427
Research Article

A Note on Parabolic Liouville Theorems and Blow-Up Rates for a Higher-Order Semilinear Parabolic System

Guocai Cai,1 Hongjing Pan,2 and Ruixiang Xing3

1School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
2School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
3School of Mathematics & Computational Science, Sun Yat-sen University, Guangzhou 510275, China

Received 30 May 2011; Accepted 7 September 2011

Academic Editor: Sining Zheng

Copyright © 2011 Guocai Cai 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.

Abstract

We improve some results of Pan and Xing (2008) and extend the exponent range in Liouville-type theorems for some parabolic systems of inequalities with the time variable on ℝ . As an immediate application of the parabolic Liouville-type theorems, the range of the exponent in blow-up rates for the corresponding systems is also improved.