Contrôlabilité exacte sur une partie du bord des équations de Maxwell. (Exact controllability on the boundary of Maxwell’s equations). (French) Zbl 0688.49041

Nalin, Olivier

C. R. Acad. Sci., Paris, Sér. I 309, No. 13, 811-815 (1989).

Summary: To extend to Maxwell’s equations the results proved by C. Bardos, G. Lebeau and J. Rauch [see appendix II of J. L. Lions, Exact controllability, perturbations and stabilization of distributed systems. Vol. 1: Exact controllability. (French) (1988; Zbl 0653.93002)] for the wave equation we first prove a result on the propagation of singularities for the system of Maxwell’s equations. We then deduce a characterization (with necessary and sufficient conditions of that part of the boundary on which one has to act to obtain exact controllability. We are thus able to improve results of J. E. Lagnese [SIAM J. Control Optimization 27, No.2, 374-388 (1989)].

MSC:

93B03	Attainable sets, reachability
35L50	Initial-boundary value problems for first-order hyperbolic systems
93B05	Controllability
93C20	Control/observation systems governed by partial differential equations
78A40	Waves and radiation in optics and electromagnetic theory

Keywords:

Maxwell’s equations; propagation of singularities; exact controllability

Citations:

Zbl 0653.93002