IDEAS home Printed from https://ideas.repec.org/a/hin/jnlaaa/026724.html
   My bibliography  Save this article

Robust control problems of vortex dynamics in superconducting films with Ginzburg-Landau complex systems

Author

Listed:
  • Aziz Belmiloudi

Abstract

We formulate and study robust control problems for a two-dimensional time-dependent Ginzburg-Landau model with Robin boundary conditions on phase-field parameter, which describes the phase transitions taking place in superconductor films with variable thickness. The objective of such study is to control the motion of vortices in the superconductor films by taking into account the influence of noises in data. Firstly, we introduce the perturbation problem of the nonlinear governing coupled system of equations (the deviation from the desired target). The existence and the uniqueness of the solution of the perturbation are proved as well as stability under mild assumptions. Afterwards, the robust control problems are formulated in the case when the control is in the external magnetic field and in the case when the control is in the initial condition of the vector potential. We show the existence of an optimal solution, and we also find necessary conditions for a saddle point optimality.

Suggested Citation

  • Aziz Belmiloudi, 2006. "Robust control problems of vortex dynamics in superconducting films with Ginzburg-Landau complex systems," Abstract and Applied Analysis, Hindawi, vol. 2006, pages 1-43, February.
    • Handle: RePEc:hin:jnlaaa:026724
    DOI: 10.1155/AAA/2006/26724
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/AAA/2006/026724.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/AAA/2006/026724.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/AAA/2006/26724?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:026724. 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.