IDEAS home Printed from https://ideas.repec.org/a/hin/jnlaaa/658936.html
   My bibliography  Save this article

Solutions of Smooth Nonlinear Partial Differential Equations

Author

Listed:
  • Jan Harm van der Walt

Abstract

The method of order completion provides a general and type-independent theory for the existence and basic regularity of the solutions of large classes of systems of nonlinear partial differential equations (PDEs). Recently, the application of convergence spaces to this theory resulted in a significant improvement upon the regularity of the solutions and provided new insight into the structure of solutions. In this paper, we show how this method may be adapted so as to allow for the infinite differentiability of generalized functions. Moreover, it is shown that a large class of smooth nonlinear PDEs admit generalized solutions in the space constructed here. As an indication of how the general theory can be applied to particular nonlinear equations, we construct generalized solutions of the parametrically driven, damped nonlinear Schrödinger equation in one spatial dimension.

Suggested Citation

  • Jan Harm van der Walt, 2011. "Solutions of Smooth Nonlinear Partial Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-37, June.
    • Handle: RePEc:hin:jnlaaa:658936
    DOI: 10.1155/2011/658936
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/AAA/2011/658936.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/AAA/2011/658936.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2011/658936?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:jnlaaa:658936. 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.