Abstract and Applied Analysis
Volume 2011 (2011), Article ID 635851, 20 pages
http://dx.doi.org/10.1155/2011/635851
Research Article

Initial Boundary Value Problem and Asymptotic Stabilization of the Two-Component Camassa-Holm Equation

Xiju Zong,1 Xingong Cheng,1 Zhonghua Wang,1 and Zhenlai Han2

1School of Control Science & Engineering, University of Jinan, Jinan 250022, Shandong, China
2School of Science, University of Jinan, Jinan 250022, China

Received 9 May 2011; Revised 23 June 2011; Accepted 20 July 2011

Academic Editor: Dirk Aeyels

Copyright © 2011 Xiju Zong et al. 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

The nonhomogeneous initial boundary value problem for the two-component Camassa-Holm equation, which describes a generalized formulation for the shallow water wave equation, on an interval is investigated. A local in time existence theorem and a uniqueness result are achieved. Next by using the fixed-point technique, a result on the global asymptotic stabilization problem by means of a boundary feedback law is considered.