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The existence of weak solutions for a generalized Camassa-Holm equation
Shaoyong Lai,  Qichang Xie,  Yunxi Guo,  YongHong Wu
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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