Exact internal controllability of vibrations of a thin body. (Contrôlabilité exacte interne des vibrations d’un corps mince.) (French) Zbl 0851.73044

Summary: We study by the Hilbert uniqueness method (HUM) the exact controllability of a three-dimensional body of very small thickness. Afterwards, we let the thickness parameter go to zero and we prove that the limit of the sequence of exact controls is the exact control given by HUM for the two-dimensional limit system. We prove, in particular, strong convergence results for the sequence of controls.


74M05 Control, switches and devices (“smart materials”) in solid mechanics
74H45 Vibrations in dynamical problems in solid mechanics