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

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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

Abstract
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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 & Applied Analysis, 2006, 5 (3) : 483-492. doi: 10.3934/cpaa.2006.5.483

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