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August  2010, 27(3): 1025-1035. doi: 10.3934/dcds.2010.27.1025

Well-posedness and blow-up phenomena for the interacting system of the Camassa-Holm and Degasperis-Procesi equations

Ying Fu 1, , Changzheng Qu 1, and  Yichen Ma 2,

1. 

Department of Mathematics, Northwest University, Shaanxi 710069, China, China
2. 

School of Science, Xi’an Jiaotong University, Shaanxi 710049, China

Received  November 2008 Revised  November 2009 Published  March 2010

In this paper, the well-posedness and blow up phenomena for the interacting system of the Camassa-Holm and Degasperis-Procesi equations are studied. We first establish the local well-posedness of strong solutions for the system. Then the precise blow-up scenarios for the strong solutions to the system are derived.
Keywords: Degasperis-Procesi equation, Camassa-Holm equation, blow-up phenomena., local well-posedness.
Mathematics Subject Classification: Primary: 35B30, 35G25; Secondary: 35L0.
Citation: Ying Fu, Changzheng Qu, Yichen Ma. Well-posedness and blow-up phenomena for the interacting system of the Camassa-Holm and Degasperis-Procesi equations. Discrete & Continuous Dynamical Systems, 2010, 27 (3) : 1025-1035. doi: 10.3934/dcds.2010.27.1025
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