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Convergence analysis of the particle method for the Camassa-Holm equation

Alina Chertock Department of Mathematics, North Carolina State University Jian-Guo Liu Duke University Terrance Pendleton North Carolina State University

Mathematical Physics mathscidoc:1702.22007

Series in Contemporary Applied Mathematics, 17, 365-373, 2012.6
The purpose of this paper is to establish a new method for proving the convergence of the particle method applied to the Camassa-Holm (CH) equation. The CH equation is a strongly nonlinear, bi-Hamiltonian, completely integrable model in the context of shallow water waves. The equation admits solutions that are nonlinear superpositions of traveling waves that have a discontinuity in the first derivative at their peaks and therefore are called peakons. This behavior admits several diverse scientific applications, but introduce difficult numerical challenges. To accurately capture these solutions, one may apply the particle method to the CH equation. Using the concept of space-time bounded variation, we show that the particle solution converges to a global weak solution of the CH equation for positive Radon measure initial data. Read More: http://www.worldscientific.com/doi/abs/10.1142/9789814417099_0033
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@inproceedings{alina2012convergence,
  title={Convergence analysis of the particle method for the Camassa-Holm equation},
  author={Alina Chertock, Jian-Guo Liu, and Terrance Pendleton},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208231825623775336},
  booktitle={Series in Contemporary Applied Mathematics},
  volume={17},
  pages={365-373},
  year={2012},
}
Alina Chertock, Jian-Guo Liu, and Terrance Pendleton. Convergence analysis of the particle method for the Camassa-Holm equation. 2012. Vol. 17. In Series in Contemporary Applied Mathematics. pp.365-373. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208231825623775336.
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