The existence of weak solutions for a generalized Camassa-Holm equation
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2011Type
Journal Article
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Lai, Shaoyong and Xie, Qichang and Guo, Yunxi and Wu, Yong Hong. 2011. The existence of weak solutions for a generalized Camassa-Holm equation. Communications on Pure and Applied Analysis. 10 (1): pp. 45-57.
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Communications on Pure and Applied Analysis
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School
Department of Mathematics and Statistics
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Abstract
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 <= s <= 3/2 is established by using the techniques of the pseudoparabolic regularization and some prior estimates derived from the equation itself.
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