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Control of the plate equation in the presence of strictly convex obstacles. (Contrôle de l’équation des plaques en présence d’obstacles strictement convexes.) (French) Zbl 0930.93007
Summary: Assuming that the Hamiltonian flow is “strongly hyperbolic”, we study the exact controllability of the plate equation in a domain containing strictly convex obstacles, with a control acting only on the trace of the Laplacian on the exterior boundary of the domain. We show that for any time \(T>0\), any initial data \((u|_{t= 0},\partial_t u|_{t= 0})\in H^{1+ \varepsilon}_0\times H^{-1+ \varepsilon}(\varepsilon> 0)\) can be controlled to zero in time \(T\).

MSC:
93B05 Controllability
74K20 Plates
35B37 PDE in connection with control problems (MSC2000)
74M05 Control, switches and devices (“smart materials”) in solid mechanics
35J15 Second-order elliptic equations
93C20 Control/observation systems governed by partial differential equations
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References:
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