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.
Yujuan Wang. Yongduan Song. Hamid Reza Karimi. "On the Global Dissipative and Multipeakon Dissipative Behavior of the Two-Component Camassa-Holm System." Abstr. Appl. Anal. 2014 (SI42) 1 - 16, 2014. https://doi.org/10.1155/2014/348695