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Issue ESAIM: COCV
Volume 5, 2000
Page(s) 87 - 137
DOI 10.1051/cocv:2000103

DOI: 10.1051/cocv:2000103

ESAIM: COCV, January 2000, Vol. 5, p. 87-137

Contrôle et stabilisation d'ondes électromagnétiques

Controllability and stabilization of electromagnetic waves

Kim Dang Phung
Centre de Mathématiques et leurs Applications, CMLA, École Normale Supérieure de Cachan, ENS, Cachan, France; (phung@cmla.ens-cachan.fr)[*]

Reçu le 4 février 1998. Révisé le 27 octobre 1998, le 18 février et le 13 septembre 1999.

Abstract: We consider the exact controllability and stabilization of Maxwell equation by using results on the propagation of singularities of the electromagnetic field. We will assume geometrical control condition and use techniques of the work of Bardos et al. on the wave equation. The problem of internal stabilization will be treated with more attention because the condition divE=0 is not preserved by the system of Maxwell with Ohm's law.

Résumé: Nous étudions la contrôlabilité exacte et la stabilisation des équations de Maxwell par le biais de la propagation des singularités du champ électromagnétique dans un domaine borné. Les résultats présentés s'inspirent des travaux de Bardos et al. sur le contrôle géométrique. Notre intéret se portera plus particulièrement sur la stabilisation interne où l'on doit considérer le système de Maxwell avec loi d'Ohm avec une densité de charge non nulle.

Keywords and phrases: Contrôlabilité, stabilisation, équation de Maxwell.

AMS Subject Classification: 93B05, 93B07, 35B40, 35Q60.

Article without figures.

Copyright EDP Sciences, SMAI



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