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Error estimate of the particle method for the b-equation

Yong Duan University of Electronic Science and Technology of China Jian-Guo Liu Duke University

Analysis of PDEs mathscidoc:1702.03025

Methods & Applications of Analysis, 23, (2), 119–154, 2016.6
In this paper, we establish the optimal error estimate of the particle method for a family of nonlinear evolutionary partial differential equations, or the so-called b-equation. The b-equation, including the Camassa-Holm equation and the Degasperis-Procesi equation, has many applications in diverse scientific fields. The particle method is an approximation of the b-equation in Lagrangian representation. We also prove short-time existence, uniqueness and regularity of the Lagrangian representation of the b-equation.
Camassa-Holm equation, Degasperis-Procesi equation, Lagrangian representation, classical solution, particle method, peakon solutions, error estimate.
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@inproceedings{yong2016error,
  title={Error estimate of the particle method for the b-equation},
  author={Yong Duan, and Jian-Guo Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207223113279764270},
  booktitle={Methods & Applications of Analysis},
  volume={23},
  number={2},
  pages={119–154},
  year={2016},
}
Yong Duan, and Jian-Guo Liu. Error estimate of the particle method for the b-equation. 2016. Vol. 23. In Methods & Applications of Analysis. pp.119–154. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207223113279764270.
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