IDEAS home Printed from https://ideas.repec.org/a/hin/jnlaaa/278542.html
   My bibliography  Save this article

Exact Asymptotic Expansion of Singular Solutions for the ( )-D Protter Problem

Author

Listed:
  • Lubomir Dechevski
  • Nedyu Popivanov
  • Todor Popov

Abstract

We study three-dimensional boundary value problems for the nonhomogeneous wave equation, which are analogues of the Darboux problems in . In contrast to the planar Darboux problem the three-dimensional version is not well posed, since its homogeneous adjoint problem has an infinite number of classical solutions. On the other hand, it is known that for smooth right-hand side functions there is a uniquely determined generalized solution that may have a strong power-type singularity at one boundary point. This singularity is isolated at the vertex of the characteristic light cone and does not propagate along the cone. The present paper describes asymptotic expansion of the generalized solutions in negative powers of the distance to this singular point. We derive necessary and sufficient conditions for existence of solutions with a fixed order of singularity and give a priori estimates for the singular solutions.

Suggested Citation

  • Lubomir Dechevski & Nedyu Popivanov & Todor Popov, 2012. "Exact Asymptotic Expansion of Singular Solutions for the ( )-D Protter Problem," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-33, September.
    • Handle: RePEc:hin:jnlaaa:278542
    DOI: 10.1155/2012/278542
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/AAA/2012/278542.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/AAA/2012/278542.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2012/278542?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
    ---><---

    Citations

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


    Cited by:

    1. Peter J. Zeitsch, 2018. "On the Riemann Function," Mathematics, MDPI, vol. 6(12), pages 1-31, December.

    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:jnlaaa:278542. 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.