Boundary observability, controllability, and stabilization of linear elastodynamic systems

摘要

In 1988 Lions obtained observability and exact controllability results for linear homogeneous isotropic elastodynamic systems. Applying some new identities we extend his theorems to nonisotropic systems. In 1991 Lagnese obtained uniform stabilizability results for two-dimensional linear homogeneous isotropic systems by applying a somewhat artificial feedback. Then he asked whether analogous results hold for a natural and physically implementable boundary feedback. Using some new identities and applying a method introduced in 1987 by Zuazua and the second author, we give an affirmative answer to this question in all dimensions and also for nonisotropic systems. Moreover, we obtain good decay estimates. Finally, applying a recent general method of uniform stabilization, we construct boundary feedbacks leading to arbitrarily large energy decay rates.