Access to the text (HTML) Access to the text (HTML)
PDF Access to the PDF text

Access to the full text of this article requires a subscription.
  • If you are a subscriber, please sign in 'My Account' at the top right of the screen.

  • If you want to subscribe to this journal, see our rates

  • You can purchase this item in Pay Per ViewPay per View - FAQ : 30,00 € Taxes included to order
    Pages Iconography Videos Other
    6 0 0 0

Comptes Rendus Mathématique
Volume 343, n° 3
pages 213-218 (août 2006)
Doi : 10.1016/j.crma.2006.06.015
Received : 16 January 2006 ;  accepted : 13 June 2006
Un problème dʼoptimisation de forme pour la contrôlabilité exacte de lʼéquation des ondes 2D
Optimal design of the support of the control for the 2D wave equation

Arnaud Münch
Laboratoire de mathématiques de Besançon, UMR CNRS 6623, 16, route de Gray, 25030 Besançon cedex, France 


On considère lʼéquation des ondes homogène posée sur   et  . On désigne par   le contrôle distribué de norme   minimale obtenu par la méthode HUM et stabilisant le système à lʼinstant  . Cette Note adresse la question de la position optimale du support miniminisant  . Supposant  , on exprime la dérivée de forme de J en terme dʼune intégrale curviligne sur (indépendamment de toute solution adjointe) permettant de mettre en place un algorithme de gradient. Une application numérique est donnée. Pour citer cet article : A. Münch, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

The full text of this article is available in PDF format.

We consider the wave equation defined on   and  . We designate by   the distributed control of minimal   norm obtained with the Hilbert Uniqueness Method which stabilizes the system at time  . This Note addresses the question of the optimal position of in order to minimize  . Assuming  , we express the shape derivative of J as a curvilinear integral on (independently of any adjoint solution) leading to a descent algorithm. A numerical application is given. To cite this article: A. Münch, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

The full text of this article is available in PDF format.

© 2006  Académie des sciences@@#104156@@
EM-CONSULTE.COM is registrered at the CNIL, déclaration n° 1286925.
As per the Law relating to information storage and personal integrity, you have the right to oppose (art 26 of that law), access (art 34 of that law) and rectify (art 36 of that law) your personal data. You may thus request that your data, should it be inaccurate, incomplete, unclear, outdated, not be used or stored, be corrected, clarified, updated or deleted.
Personal information regarding our website's visitors, including their identity, is confidential.
The owners of this website hereby guarantee to respect the legal confidentiality conditions, applicable in France, and not to disclose this data to third parties.
Article Outline
You can move this window by clicking on the headline