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

Yujuan Wang, Yongduan Song and Hamid Reza Karimi

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: 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.

Date: 2014
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https://doi.org/10.1155/2014/348695

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:348695

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