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May  2016, 36(5): 2613-2625. doi: 10.3934/dcds.2016.36.2613

## Persistence properties and unique continuation for a dispersionless two-component Camassa-Holm system with peakon and weak kink solutions

 1 Department of Mathematics, South China Agricultural University, 510642 Guangzhou, China 2 Department of Mathematics, University of Texas Pan American, 78541 Edinburg, TX, United States

Received  April 2015 Revised  May 2015 Published  October 2015

In this paper, we study the persistence properties and unique continuation for a dispersionless two-component system with peakon and weak kink solutions. These properties guarantee strong solutions of the two-component system decay at infinity in the spatial variable provided that the initial data satisfies the condition of decaying at infinity. Furthermore, we give an optimal decaying index of the momentum for the system and show that the system exhibits unique continuation if the initial momentum $m_0$ and $n_0$ are non-negative.
Citation: Qiaoyi Hu, Zhijun Qiao. Persistence properties and unique continuation for a dispersionless two-component Camassa-Holm system with peakon and weak kink solutions. Discrete & Continuous Dynamical Systems - A, 2016, 36 (5) : 2613-2625. doi: 10.3934/dcds.2016.36.2613
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