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Abstract and Applied Analysis
Volume 2011 (2011), Article ID 285040, 15 pages
doi:10.1155/2011/285040
The Local Strong and Weak Solutions for a Nonlinear Dissipative Camassa-Holm Equation
Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu, 610074, China
Received 17 January 2011; Revised 3 August 2011; Accepted 8 August 2011
Academic Editor: Yuri V. Rogovchenko
Copyright © 2011 Shaoyong Lai. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Using the Kato theorem for abstract differential equations, the local well-posedness of the solution for a nonlinear dissipative Camassa-Holm equation is established in space with . In addition, a sufficient condition for the existence of weak solutions of the equation in lower order Sobolev space with is developed.