# American Institute of Mathematical Sciences

October  2012, 32(10): 3459-3484. doi: 10.3934/dcds.2012.32.3459

## Wave breaking phenomena and global solutions for a generalized periodic two-component Camassa-Holm system

 1 Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019-0408, United States 2 Department of Mathematics and Physics, Huaiyin Institute of Technology, Huaiyin, Jiangsu 223003, China

Received  April 2011 Revised  January 2012 Published  May 2012

Considered herein is the generalized two-component periodic Camassa-Holm system. The precise blow-up scenarios of strong solutions and several results of blow-up solutions with certain initial profiles are described in detail. The exact blow-up rates are also determined. Finally, a sufficient condition for global solutions is established.
Citation: Caixia Chen, Shu Wen. Wave breaking phenomena and global solutions for a generalized periodic two-component Camassa-Holm system. Discrete & Continuous Dynamical Systems, 2012, 32 (10) : 3459-3484. doi: 10.3934/dcds.2012.32.3459
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