The existence of weak solutions for a generalized Camassa-Holm equation
Shaoyong Lai Qichang Xie Yunxi Guo YongHong Wu
Communications on Pure & Applied Analysis 2011, 10(1): 45-57 doi: 10.3934/cpaa.2011.10.45
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.
keywords: high order nonlinear terms pseudoparabolic regularization technique. weak solution Generalized Camassa-Holm equation

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