IDEAS home Printed from https://ideas.repec.org/a/bla/mathna/v297y2024i2p525-548.html
   My bibliography  Save this article

Well‐posedness and asymptotic behavior for a p‐biharmonic pseudo‐parabolic equation with logarithmic nonlinearity of the gradient type

Author

Listed:
  • Mengyuan Zhang
  • Zhiqing Liu
  • Xinli Zhang

Abstract

This paper is concerned with the well‐posedness and asymptotic behavior for an initial boundary value problem of a pseudo‐parabolic equation with p‐biharmonic operator and logarithmic nonlinearity of the gradient type. The existence of the global weak solution is established by combining the technique of potential‐well and the method of Faedo–Galerkin approximation. Meantime, by virtue of the improved logarithmic Sobolev inequality and modified differential inequality, we obtain the results on infinite and finite time blow‐up and derive the lifespan of blow‐up solutions in various energy levels. Furthermore, the extinction phenomenon with extinction time is presented.

Suggested Citation

  • Mengyuan Zhang & Zhiqing Liu & Xinli Zhang, 2024. "Well‐posedness and asymptotic behavior for a p‐biharmonic pseudo‐parabolic equation with logarithmic nonlinearity of the gradient type," Mathematische Nachrichten, Wiley Blackwell, vol. 297(2), pages 525-548, February.
    • Handle: RePEc:bla:mathna:v:297:y:2024:i:2:p:525-548
    DOI: 10.1002/mana.202200264
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/mana.202200264
    Download Restriction: no
    File URL: https://libkey.io/10.1002/mana.202200264?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:bla:mathna:v:297:y:2024:i:2:p:525-548. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0025-584X .

    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.