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

Publication ,  Journal Article
Duan, Y; Liu, JG
Published in: Discrete and Continuous Dynamical Systems- Series A
May 1, 2014
Published version (DOI)

In this paper, 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.

Duke Scholars

Jian-Guo Liu
Author Jian-Guo Liu Physics

Published In

Discrete and Continuous Dynamical Systems- Series A

DOI

10.3934/dcds.2014.34.1995

EISSN

1553-5231

ISSN

1078-0947

Publication Date

May 1, 2014

Volume

34

Issue

5

Start / End Page

1995 / 2011

Related Subject Headings

  • Applied Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

Citation

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ICMJE
MLA
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Duan, Y., & Liu, J. G. (2014). Convergence analysis of the vortex blob method for the b-equation. Discrete and Continuous Dynamical Systems- Series A, 34(5), 1995–2011. https://doi.org/10.3934/dcds.2014.34.1995
Duan, Y., and J. G. Liu. “Convergence analysis of the vortex blob method for the b-equation.” Discrete and Continuous Dynamical Systems- Series A 34, no. 5 (May 1, 2014): 1995–2011. https://doi.org/10.3934/dcds.2014.34.1995.
Duan Y, Liu JG. Convergence analysis of the vortex blob method for the b-equation. Discrete and Continuous Dynamical Systems- Series A. 2014 May 1;34(5):1995–2011.
Duan, Y., and J. G. Liu. “Convergence analysis of the vortex blob method for the b-equation.” Discrete and Continuous Dynamical Systems- Series A, vol. 34, no. 5, May 2014, pp. 1995–2011. Scopus, doi:10.3934/dcds.2014.34.1995.
Duan Y, Liu JG. Convergence analysis of the vortex blob method for the b-equation. Discrete and Continuous Dynamical Systems- Series A. 2014 May 1;34(5):1995–2011.

Published In

Discrete and Continuous Dynamical Systems- Series A

DOI

10.3934/dcds.2014.34.1995

EISSN

1553-5231

ISSN

1078-0947

Publication Date

May 1, 2014

Volume

34

Issue

5

Start / End Page

1995 / 2011

Related Subject Headings

  • Applied Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics