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Zbl 1237.35139
Li, Nan; Lai, Shaoyong; Li, Shuang; Wu, Meng
The local and global existence of solutions for a generalized Camassa-Holm equation. (English)
[J] Abstr. Appl. Anal. 2012, Article ID 532369, 26 p. (2012). ISSN 1085-3375; ISSN 1687-0409/e

Summary: A nonlinear generalization of the Camassa-Holm equation is investigated. By making use of the pseudoparabolic regularization technique, its local well posedness in Sobolev space $H^s(\bbfR)$ with $s > 3/2$ is established via a limiting procedure. Provided that the initial value $u_0$ satisfies the sign condition and $u_0 \in H^s (\bbfR)$ ($s > 3/2$), it is shown that there exists a unique global solution for the equation in space $C([0, \infty); H^s(\bbfR)) \cap C^1([0, \infty); H^{s-1}(\bbfR))$.

MSC 2000:: *35Q53 KdV-like equations
35Q51 Solitons
35A02

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Zentralblatt MATH Berlin [Germany]