American Institute of Mathematical Sciences

January  2011, 10(1): 45-57. doi: 10.3934/cpaa.2011.10.45

The existence of weak solutions for a generalized Camassa-Holm equation

 1 Department of Mathematics,Sichuan Normal University, Chengdu, Department of Mathematics and Statistics,Curtin University of Technology, Perth, China 2 Department of Applied Mathematics, Southwestern University of Finance and Economics, 610074, Chengdu, China, China, China

Received  October 2009 Revised  August 2010 Published  November 2010

A Camassa-Holm type equation containing nonlinear dissipative effect is investigated. A sufficient condition which guarantees the existence of weak solutions of the equation in lower order Sobolev space $H^s$ with $1 \leq s \leq \frac{3}{2}$ is established by using the techniques of the pseudoparabolic regularization and some prior estimates derived from the equation itself.
Citation: Shaoyong Lai, Qichang Xie, Yunxi Guo, YongHong Wu. The existence of weak solutions for a generalized Camassa-Holm equation. Communications on Pure & Applied Analysis, 2011, 10 (1) : 45-57. doi: 10.3934/cpaa.2011.10.45
References:
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References:
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