IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i5p468-d505516.html
   My bibliography  Save this article

On a Semilinear Parabolic Problem with Four-Point Boundary Conditions

Author

Listed:
  • Marián Slodička

    (Research Group NaM 2 , Department of Electronics and Information Systems, Ghent University, Krijgslaan 281, 9000 Ghent, Belgium)

Abstract

This paper studies a semilinear parabolic equation in 1D along with nonlocal boundary conditions. The value at each boundary point is associated with the value at an interior point of the domain, which is known as a four-point boundary condition. First, the solvability of a steady-state problem is addressed and a constructive algorithm for finding a solution is proposed. Combining this schema with the semi-discretization in time, a constructive algorithm for approximation of a solution to a transient problem is developed. The well-posedness of the problem is shown using the semigroup theory in C -spaces. Numerical experiments support the theoretical algorithms.

Suggested Citation

  • Marián Slodička, 2021. "On a Semilinear Parabolic Problem with Four-Point Boundary Conditions," Mathematics, MDPI, vol. 9(5), pages 1-15, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:468-:d:505516
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/5/468/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/5/468/
    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:9:y:2021:i:5:p:468-:d:505516. 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.