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A new asymptotic behavior of solutions to the Camassa-Holm equation


Authors: Lidiao Ni and Yong Zhou
Journal: Proc. Amer. Math. Soc. 140 (2012), 607-614
MSC (2010): Primary 37L05; Secondary 35Q58, 26A12
DOI: https://doi.org/10.1090/S0002-9939-2011-10922-5
Published electronically: May 12, 2011
MathSciNet review: 2846329
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Abstract: The present work is mainly concerned with an algebraic decay rate of the strong solution to the Camassa-Holm equation in $ L^{\infty}$-space. In particular, it is proved that the solution decays algebraically with the same exponent as that of the initial datum.


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Additional Information

Lidiao Ni
Affiliation: Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, People’s Republic of China
Email: ni.lidiao@gmail.com

Yong Zhou
Affiliation: Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, People’s Republic of China
Email: yzhoumath@zjnu.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-2011-10922-5
Keywords: Camassa-Holm equation, asymptotic behavior
Received by editor(s): April 21, 2010
Received by editor(s) in revised form: November 28, 2010
Published electronically: May 12, 2011
Additional Notes: The second author is the corresponding author and is partially supported by the Zhejiang Innovation Project (Grant No. T200905), ZJNSF (Grant No. R6090109) and NSFC (Grant No. 10971197)
Communicated by: Walter Craig
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.