IDEAS home Printed from https://ideas.repec.org/a/hin/jnlaaa/647368.html
   My bibliography  Save this article

Wave Breaking and Propagation Speed for a Class of One-Dimensional Shallow Water Equations

Author

Listed:
  • Zaihong Jiang
  • Sevdzhan Hakkaev

Abstract

We investigate a more general family of one-dimensional shallow water equations. Analogous to the Camassa-Holm equation, these new equations admit blow-up phenomenon and infinite propagation speed. First, we establish blow-up results for this family of equations under various classes of initial data. It turns out that it is the shape instead of the size and smoothness of the initial data which influences breakdown in finite time. Then, infinite propagation speed for the shallow water equations is proved in the following sense: the corresponding solution with compactly supported initial datum does not have compact -support any longer in its lifespan.

Suggested Citation

  • Zaihong Jiang & Sevdzhan Hakkaev, 2011. "Wave Breaking and Propagation Speed for a Class of One-Dimensional Shallow Water Equations," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-15, November.
    • Handle: RePEc:hin:jnlaaa:647368
    DOI: 10.1155/2011/647368
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/AAA/2011/647368.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/AAA/2011/647368.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2011/647368?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hin:jnlaaa:647368. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.