IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i14p3137-d1195148.html
   My bibliography  Save this article

Classical Solutions of Hyperbolic Equation with Translation Operators in Free Terms

Author

Listed:
  • Vladimir Vasilyev

    (Center of Applied Mathematics, Belgorod State National Research University, Pobedy St. 85, Belgorod 308015, Russia)

  • Natalya Zaitseva

    (Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow 119991, Russia)

Abstract

In this paper, we study the question of constructing explicit solutions in a half-space of a hyperbolic equation containing translation operators in space variables in all coordinate directions. Such equations are a natural generalization of classical equations of hyperbolic type, and the resulting solution relates the value of the desired function at different points of the half-space where the process takes place. To construct solutions, a classical operating scheme is used, namely, the formal application of an integral transformation. A theorem is proved that the constructed solutions are classical if the real part of the symbol of the differential-difference operator in the equation is positive. Classes of equations for which this condition is satisfied are given.

Suggested Citation

  • Vladimir Vasilyev & Natalya Zaitseva, 2023. "Classical Solutions of Hyperbolic Equation with Translation Operators in Free Terms," Mathematics, MDPI, vol. 11(14), pages 1-9, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3137-:d:1195148
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/14/3137/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/14/3137/
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Vladimir Vasilyev & Natalya Zaitseva, 2024. "On Hyperbolic Equations with a Translation Operator in Lowest Derivatives," Mathematics, MDPI, vol. 12(12), pages 1-8, June.

    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:11:y:2023:i:14:p:3137-:d:1195148. 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.