Journal of Applied Mathematics
Volume 2012 (2012), Article ID 197672, 20 pages
http://dx.doi.org/10.1155/2012/197672
Research Article

On the Blow-Up of Solutions of a Weakly Dissipative Modified Two-Component Periodic Camassa-Holm System

Yongsheng Mi,1,2 Chunlai Mu,1 and Weian Tao2

1College of Mathematics and Statistics, Chongqing University, Chongqing 400044, China
2College of Mathematics and Computer Sciences, Yangtze Normal University, Fuling, Chongqing 408100, China

Received 16 May 2012; Revised 24 July 2012; Accepted 30 July 2012

Academic Editor: Ferenc Hartung

Copyright © 2012 Yongsheng Mi 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 study the Cauchy problem of a weakly dissipative modified two-component periodic Camassa-Holm equation. We first establish the local well-posedness result. Then we derive the precise blow-up scenario and the blow-up rate for strong solutions to the system. Finally, we present two blow-up results for strong solutions to the system.