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

Alabau, Fatiha; Komornik, Vilmos

C. R. Acad. Sci., Paris, Sér. I 324, No. 5, 519-524 (1997).

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

Keywords:

Hilbert uniqueness method; boundary feedbacks; exponential energy decay