IDEAS home Printed from https://ideas.repec.org/a/hin/jnijde/315421.html
   My bibliography  Save this article

On the Speed of Spread for Fractional Reaction-Diffusion Equations

Author

Listed:
  • Hans Engler

Abstract

The fractional reaction diffusion equation 𠜕 ð ‘¡ ð ‘¢ + ð ´ ð ‘¢ = ð ‘” ( ð ‘¢ ) is discussed, where ð ´ is a fractional differential operator on â„ of order ð ›¼ ∈ ( 0 , 2 ) , the ð ¶ 1 function ð ‘” vanishes at ð œ = 0 and ð œ = 1 , and either ð ‘” ≥ 0 on ( 0 , 1 ) or ð ‘” < 0 near ð œ = 0 . In the case of nonnegative g, it is shown that solutions with initial support on the positive half axis spread into the left half axis with unbounded speed if ð ‘” ( ð œ ) satisfies some weak growth condition near ð œ = 0 in the case ð ›¼ > 1 , or if ð ‘” is merely positive on a sufficiently large interval near ð œ = 1 in the case ð ›¼ < 1 . On the other hand, it shown that solutions spread with finite speed if ð ‘” î…ž ( 0 ) < 0 . The proofs use comparison arguments and a suitable family of travelling wave solutions.

Suggested Citation

  • Hans Engler, 2010. "On the Speed of Spread for Fractional Reaction-Diffusion Equations," International Journal of Differential Equations, Hindawi, vol. 2010, pages 1-16, November.
  • Handle: RePEc:hin:jnijde:315421
    DOI: 10.1155/2010/315421
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/IJDE/2010/315421.pdf
    Download Restriction: no

    File URL: http://downloads.hindawi.com/journals/IJDE/2010/315421.xml
    Download Restriction: no

    File URL: https://libkey.io/10.1155/2010/315421?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
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Cayama, Jorge & Cuesta, Carlota M. & de la Hoz, Francisco, 2021. "A pseudospectral method for the one-dimensional fractional Laplacian on R," Applied Mathematics and Computation, Elsevier, vol. 389(C).
    2. Che, Han & Wang, Yu-Lan & Li, Zhi-Yuan, 2022. "Novel patterns in a class of fractional reaction–diffusion models with the Riesz fractional derivative," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 149-163.

    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:jnijde:315421. 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.