IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i23p4498-d987185.html
   My bibliography  Save this article

Well-Posedness and Exponential Stability of Swelling Porous with Gurtin–Pipkin Thermoelasticity

Author

Listed:
  • Tijani Abdul-Aziz Apalara

    (Department of Mathematics, University of Hafr Al-Batin (UHB), Hafr Al-Batin 31991, Saudi Arabia)

  • Ohud Bulayhan Almutairi

    (Department of Mathematics, University of Hafr Al-Batin (UHB), Hafr Al-Batin 31991, Saudi Arabia)

Abstract

The focus of this work is to investigate the well-posedness and exponential stability of a swelling porous system with the Gurtin–Pipkin thermal effect as the only source of damping. The well-posedness result is achieved using an essential corollary to the Lumer–Phillips Theorem. By constructing a suitable Lyapunov functional, we establish an exponential stability result without the conventional limitation to the system’s parameters (coined a stability number in the literature). Generally, the study demonstrates that the unique dissipation from the Gurtin–Pipkin thermal law is sufficient to stabilize the system exponentially, irrespective of the system’s parameters.

Suggested Citation

  • Tijani Abdul-Aziz Apalara & Ohud Bulayhan Almutairi, 2022. "Well-Posedness and Exponential Stability of Swelling Porous with Gurtin–Pipkin Thermoelasticity," Mathematics, MDPI, vol. 10(23), pages 1-17, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4498-:d:987185
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/23/4498/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/23/4498/
    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:10:y:2022:i:23:p:4498-:d:987185. 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.