IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v161y2014i3d10.1007_s10957-013-0447-9.html
   My bibliography  Save this article

Optimal Design of the Time-Dependent Support of Bang–Bang Type Controls for the Approximate Controllability of the Heat Equation

Author

Listed:
  • Francisco Periago

    (Universidad Politécnica de Cartagena)

Abstract

We consider the nonlinear optimal shape design problem, which consists in minimizing the amplitude of bang–bang type controls for the approximate controllability of a linear heat equation with a bounded potential. The design variable is the time-dependent support of the control. Precisely, we look for the best space–time shape and location of the support of the control among those, which have the same Lebesgue measure. Since the admissibility set for the problem is not convex, we first obtain a well-posed relaxation of the original problem and then use it to derive a descent method for the numerical resolution of the problem. Numerical experiments in 2D suggest that, even for a regular initial datum, a true relaxation phenomenon occurs in this context. Also, we implement a simple algorithm for computing a quasi-optimal domain for the original problem from the optimal solution of its associated relaxed one.

Suggested Citation

  • Francisco Periago, 2014. "Optimal Design of the Time-Dependent Support of Bang–Bang Type Controls for the Approximate Controllability of the Heat Equation," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 951-968, June.
    • Handle: RePEc:spr:joptap:v:161:y:2014:i:3:d:10.1007_s10957-013-0447-9
    DOI: 10.1007/s10957-013-0447-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-013-0447-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-013-0447-9?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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:spr:joptap:v:161:y:2014:i:3:d:10.1007_s10957-013-0447-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.