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September  2006, 5(3): 483-492. doi: 10.3934/cpaa.2006.5.483

The study on solutions to Camassa-Holm equation with weak dissipation

Danping Ding 1, , Lixin Tian 1, and  Gang Xu 1,

1. 

Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China, China, China

Received  May 2005 Revised  February 2006 Published  June 2006

This paper investigates the existence of solution on the weak dissipative Camassa-Holm equation, and studies the dynamical behaviors of the solution for this equation. An interesting result is given that the solution for the Cauchy problem on weak dissipative Camassa-Holm equation is local under certain conditions. Moreover, discussions on solitary solution to weak dissipation Camassa-Holm equation are given.
Keywords: blow-up, Weak dissipation Camassa-Holm equation, solitary..
Mathematics Subject Classification: 35A07, 35B10, 35B45, 35L0.
Citation: Danping Ding, Lixin Tian, Gang Xu. The study on solutions to Camassa-Holm equation with weak dissipation. Communications on Pure and Applied Analysis, 2006, 5 (3) : 483-492. doi: 10.3934/cpaa.2006.5.483
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