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Controllability of a coupled wave system with a single control and different speeds

Lissy, Pierre; Niu, Jingrui (2022), Controllability of a coupled wave system with a single control and different speeds. https://basepub.dauphine.psl.eu/handle/123456789/23294

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Type
Document de travail / Working paper
Date
2022
Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Published in
Paris
Pages
53
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Author(s)
Lissy, Pierre
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Niu, Jingrui cc
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Abstract (EN)
We consider an exact controllability problem in a smooth bounded domain Ω of R d , d ∈ N * , for a coupled wave system, with two different speeds and a single control acting on an open subset ω satisfying the Geometric Control Condition and acting on one speed only. Actions for the wave equations with the second speed are obtained through a coupling term. Firstly, we construct appropriate state spaces with compatibility conditions associated with the coupling structure. Secondly, in these well-prepared spaces, we prove that the coupled wave system is exactly controllable if and only if the coupling structure satisfies an operator Kalman rank condition.
Subjects / Keywords
Wave equation; controllability; unique continuation; coupled system