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Abstract and Applied Analysis
Volume 2014, Article ID 348695, 16 pages
Research Article

On the Global Dissipative and Multipeakon Dissipative Behavior of the Two-Component Camassa-Holm System

1School of Automation, Chongqing University, Chongqing 400044, China
2Department of Engineering, Faculty of Engineering and Science, University of Agder, 4898 Grimstad, Norway

Received 14 February 2014; Revised 20 March 2014; Accepted 20 March 2014; Published 4 May 2014

Academic Editor: Bo Shen

Copyright © 2014 Yujuan Wang 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.


The global dissipative and multipeakon dissipative behavior of the two-component Camassa-Holm shallow water system after wave breaking was studied in this paper. The underlying approach is based on a skillfully defined characteristic and a set of newly introduced variables which transform the original system into a Lagrangian semilinear system. It is the transformation, together with the associated properties, that allows for the continuity of the solution beyond collision time to be established, leading to a uniquely global dissipative solution, which constructs a semigroup, and the multipeakon dissipative solution.