IDEAS home Printed from https://ideas.repec.org/a/wsi/fracta/v31y2023i10ns0218348x2340193x.html
   My bibliography  Save this article

Well-Posedness And Regularization For Nonlocal Diffusion Equation With Riemann–Liouville Derivative

Author

Listed:
  • RENHAI WANG

    (School of Mathematical Sciences, Guizhou Normal University, Guiyang 550001, P. R. China)

  • HOANG VAN DAI

    (Faculty of Mathematics and Computer Science, University of Science, Ho Chi Minh City, Vietnam3Vietnam National University, Ho Chi Minh City, Vietnam)

  • NGUYEN ANH TUAN

    (Division of Applied Mathematics, Science and Technology Advanced Institute, Van Lang University, Ho Chi Minh City, Vietnam5Faculty of Applied Technology, School of Technology, Van Lang University, Ho Chi Minh City, Vietnam)

  • NGUYEN HUU CAN

    (Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam)

Abstract

In this paper, we are interested in studying the fractional diffusion equation with Riemann–Liouville as follows: D0+αy − y xx = 0, 0 < x < π, with nonlocal in time condition. We are going to study the well-posedness of the above problem with some assumptions of the input data. On the other hand, in Hilbert scale and Lp spaces, we provide several estimates of regularity results of the mild solution. We also establish the evaluation for gradient term of the mild solution. We also show that the nonlocal problem is ill-posed in the sense of Hadamard. We also derive the regularity result by applying Fourier truncation method. The main tool of the paper is to use some estimates of Wright functions and Sobolev embeddings. In addition, we also obtain a lower bound of the solution according to the input data.

Suggested Citation

  • Renhai Wang & Hoang Van Dai & Nguyen Anh Tuan & Nguyen Huu Can, 2023. "Well-Posedness And Regularization For Nonlocal Diffusion Equation With Riemann–Liouville Derivative," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(10), pages 1-13.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:10:n:s0218348x2340193x
    DOI: 10.1142/S0218348X2340193X
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0218348X2340193X
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0218348X2340193X?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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:wsi:fracta:v:31:y:2023:i:10:n:s0218348x2340193x. 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: Tai Tone Lim (email available below). General contact details of provider: https://www.worldscientific.com/worldscinet/fractals .

    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.