IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i18p2895-d1479467.html
   My bibliography  Save this article

The Second Critical Exponent for a Time-Fractional Reaction-Diffusion Equation

Author

Listed:
  • Takefumi Igarashi

    (Department of Liberal Arts and Science, College of Science and Technology, Nihon University, 7-24-1, Narashino-dai, Funabashi 274-8501, Chiba, Japan)

Abstract

In this paper, we consider the Cauchy problem of a time-fractional nonlinear diffusion equation. According to Kaplan’s first eigenvalue method, we first prove the blow-up of the solutions in finite time under some sufficient conditions. We next provide sufficient conditions for the existence of global solutions by using the results of Zhang and Sun. In conclusion, we find the second critical exponent for the existence of global and non-global solutions via the decay rates of the initial data at spatial infinity.

Suggested Citation

  • Takefumi Igarashi, 2024. "The Second Critical Exponent for a Time-Fractional Reaction-Diffusion Equation," Mathematics, MDPI, vol. 12(18), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:18:p:2895-:d:1479467
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/18/2895/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/18/2895/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:12:y:2024:i:18:p:2895-:d:1479467. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.