IDEAS home Printed from https://ideas.repec.org/a/hin/jjmath/5553126.html
   My bibliography  Save this article

Existence and Uniqueness of Weak Solutions for Novel Anisotropic Nonlinear Diffusion Equations Related to Image Analysis

Author

Listed:
  • Anas Tiarimti Alaoui
  • Mostafa Jourhmane
  • Sun Young Cho

Abstract

This paper establishes the existence and uniqueness of weak solutions for the initial-boundary value problem of anisotropic nonlinear diffusion partial differential equations related to image processing and analysis. An implicit iterative method combined with a variational approach has been applied to construct approximate solutions for this problem. Then, under some a priori estimates and a monotonicity condition, the existence of unique weak solutions for this problem has been proven. This work has been complemented by a consistent and stable approximation scheme showing its great significance as an image restoration technique.

Suggested Citation

  • Anas Tiarimti Alaoui & Mostafa Jourhmane & Sun Young Cho, 2021. "Existence and Uniqueness of Weak Solutions for Novel Anisotropic Nonlinear Diffusion Equations Related to Image Analysis," Journal of Mathematics, Hindawi, vol. 2021, pages 1-18, March.
    • Handle: RePEc:hin:jjmath:5553126
    DOI: 10.1155/2021/5553126
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/jmath/2021/5553126.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/jmath/2021/5553126.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2021/5553126?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:hin:jjmath:5553126. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.