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Boundary observability, controllability and stabilization of linear elastodynamic systems. (Observabilité, contrôlabilité et stabilisation frontière du système d’élasticité linéaire.) (French. Abridged English version) Zbl 0878.73012

Summary: We study homogeneous but not necessarily isotropic linear elastodynamic systems. Applying the Hilbert uniqueness method, we establish their boundary observability and exact boundary controllability. Then we construct boundary feedbacks leading to arbitrarily large energy decay rates. Finally, under some geometrical conditions, we prove that a “natural” boundary feedback leads also to exponential energy decay.

MSC:

74B05 Classical linear elasticity
93C20 Control/observation systems governed by partial differential equations
93D15 Stabilization of systems by feedback
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