Authors

Zheng Yin, Shaoyong Lai, Yunxi Guo

Abstract

A nonlinear shallow water equation, which includes the famous Camassa–Holm (CH) and Degasperis–Procesi (DP) equations as special cases, is investigated. Provided that initial value u 0 ∈ H s ( 1 ≤ s ≤ 3 2 ) , u 0 ∈ L 1 ( R ) and ( 1 − ∂ x 2 ) u 0 does not change sign, it is shown that there exists a unique global weak solution to the equation.

Keywords

Global existence; Blow-up; Shallow water model; Local well-posedness

Citation

  • Journal: Computers & Mathematics with Applications
  • Year: 2010
  • Volume: 60
  • Issue: 9
  • Pages: 2645–2652
  • Publisher: Elsevier BV
  • DOI: 10.1016/j.camwa.2010.08.094

BibTeX

@article{Yin_2010,
  title={{Global existence of weak solutions for a shallow water equation}},
  volume={60},
  ISSN={0898-1221},
  DOI={10.1016/j.camwa.2010.08.094},
  number={9},
  journal={Computers & Mathematics with Applications},
  publisher={Elsevier BV},
  author={Yin, Zheng and Lai, Shaoyong and Guo, Yunxi},
  year={2010},
  pages={2645--2652}
}

Download the bib file

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