Convergence analysis of the vortex blob method for the b-equation

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

Analysis of PDEs mathscidoc:1702.03039

Discrete & Continuous Dynamical Systems, 34, (5), 1995 - 2011, 2014.5
Abstract We prove the convergence of the vortex blob method for a family of nonlinear evolutionary partial differential equations (PDEs), the so-called b-equation. This kind of PDEs, including the Camassa-Holm equation and the Degasperis-Procesi equation, has many applications in diverse scientific fields. Our convergence analysis also provides a proof for the existence of the global weak solution to the b-equation when the initial data is a nonnegative Radon measure with compact support.
Camassa-Holm equation, Degasperis-Procesi equation, b-equation, global weak solution, vortex blob method, space-time BV estimates, peakon solution
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@inproceedings{yong2014convergence,
  title={Convergence analysis of the vortex blob method for the b-equation},
  author={Yong Duan, and Jian-Guo Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208212021141915314},
  booktitle={Discrete & Continuous Dynamical Systems},
  volume={34},
  number={5},
  pages={1995 - 2011},
  year={2014},
}
Yong Duan, and Jian-Guo Liu. Convergence analysis of the vortex blob method for the b-equation. 2014. Vol. 34. In Discrete & Continuous Dynamical Systems. pp.1995 - 2011. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208212021141915314.
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