IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i24p3248-d703024.html
   My bibliography  Save this article

Blow-Up and Global Existence of Solutions for the Time Fractional Reaction–Diffusion Equation

Author

Listed:
  • Linfei Shi

    (Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China)

  • Wenguang Cheng

    (Department of Mathematics, Yuxi Normal University, Yuxi 653100, China)

  • Jinjin Mao

    (Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China)

  • Tianzhou Xu

    (Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China)

Abstract

In this paper, we investigate a reaction–diffusion equation with a Caputo fractional derivative in time and with boundary conditions. According to the principle of contraction mapping, we first prove the existence and uniqueness of local solutions. Then, under some conditions of the initial data, we obtain two sufficient conditions for the blow-up of the solutions in finite time. Moreover, the existence of global solutions is studied when the initial data is small enough. Finally, the long-time behavior of bounded solutions is analyzed.

Suggested Citation

  • Linfei Shi & Wenguang Cheng & Jinjin Mao & Tianzhou Xu, 2021. "Blow-Up and Global Existence of Solutions for the Time Fractional Reaction–Diffusion Equation," Mathematics, MDPI, vol. 9(24), pages 1-9, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3248-:d:703024
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/24/3248/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/24/3248/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. AHMAD, Bashir & ALSAEDI, Ahmed & KIRANE, Mokhtar, 2021. "Blowing-up Solutions of Distributed Fractional Differential Systems," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      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:9:y:2021:i:24:p:3248-:d:703024. 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.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.