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September  2004, 3(3): 501-508. doi: 10.3934/cpaa.2004.3.501

Well-posedness and blow-up phenomena for the periodic generalized Camassa-Holm equation

Zhaoyang Yin 1,

1. 

Department of Mathematics, Zhongshan University, Guangzhou, 510275

Received  February 2003 Revised  March 2004 Published  June 2004

We establish the local well-posedness for the periodic generalized Camassa-Holm equation. We also give the precise blow-up scenario and prove that the equation has smooth solutions that blow up in finite time.
Keywords: The periodic generalized Camassa-Holm equation, blow-up scenario., local well- posedness.
Mathematics Subject Classification: 35G25, 35L05.
Citation: Zhaoyang Yin. Well-posedness and blow-up phenomena for the periodic generalized Camassa-Holm equation. Communications on Pure and Applied Analysis, 2004, 3 (3) : 501-508. doi: 10.3934/cpaa.2004.3.501
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