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The local and global existence of solutions for a generalized Camassa-Holm equation. (English) Zbl 1237.35139
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:
35Q53KdV-like (Korteweg-de Vries) equations
35Q51Soliton-like equations
35A02Uniqueness problems for PDE: global uniqueness, local uniqueness, non-uniqueness
WorldCat.org
Full Text: DOI
References:
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