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

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  • 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.
    Mathematics Subject Classification: Primary: 35Q53; Secondary: 35L05.


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