F. Alabau et V. Komornik, BOUNDARY OBSERVABILITY, CONTROLLABILITY AND STABILIZATION OF LINEAR ELASTODYNAMIC SYSTEMS, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 324(5), 1997, pp. 519-524
We study homogeneous but not necessarily isotropic linear elastodynami
c systems. Applying the Hilbert Uniqueness Method (HUM), we establish
their boundary observability and their exact boundary controllability.
Then we construct boundary feedbacks leading to arbitrarily large ene
rgy decay rates. Finally, under some geometrical conditions, we prove
that a ''natural'' boundary feedback leads also to exponentiel energy
decay.