Indirect controllability of locally coupled wave-type systems and applications

Fatiha Alabau-Boussouira (1, 2, 3) , Matthieu Léautaud (4, 5)

1 LMAM - Laboratoire de Mathématiques et Applications de Metz
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
3 CORIDA - Robust control of infinite dimensional systems and applications
4 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
5 LJLL - Laboratoire Jacques-Louis Lions

We consider symmetric systems of two wave-type equations only one of them being controlled. The two equations are coupled by zero order terms, localized in part of the domain. We prove an internal and a boundary null-controllability result in any space dimension, provided that both the coupling and the control regions satisfy the Geometric Control Condition. We deduce similar null-controllability results in any positive time for parabolic systems and Schrödinger-type systems under the same geometric conditions on the coupling and the control regions. This includes several examples in which these two regions have an empty intersection.

Keywords: wave equation; controllability; Observability; parabolic systems; hyperbolic systems; geometric conditions

Domains: Mathematics [math]; Analysis of PDEs [math.AP]

Fatiha Alabau-Boussouira, Matthieu Léautaud. Indirect controllability of locally coupled wave-type systems and applications. 2011. ⟨hal-00636605⟩