## Abstract and Applied Analysis

### The Local and Global Existence of Solutions for a Generalized Camassa-Holm Equation

#### Abstract

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 ${H}^{S}(R)$ with $s>3/2$ is established via a limiting procedure. Provided that the initial value${u}_{0}$ satisfies the sign condition and ${u}_{0}\in {H}^{s}(R) (s>3/2)$, it is shown that there exists a uniqueglobal solution for the equation in space $C([0,\infty );{H}^{s}(R))\cap {C}^{1}([0,\infty );{H}^{s-1}(R))$.

#### Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 532369, 26 pages.

Dates
First available in Project Euclid: 5 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1365174041

Digital Object Identifier
doi:10.1155/2012/532369

Mathematical Reviews number (MathSciNet)
MR2910721

Zentralblatt MATH identifier
1237.35139

#### Citation

Li, Nan; Lai, Shaoyong; Li, Shuang; Wu, Meng. The Local and Global Existence of Solutions for a Generalized Camassa-Holm Equation. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 532369, 26 pages. doi:10.1155/2012/532369. https://projecteuclid.org/euclid.aaa/1365174041

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