We consider a linear coupled system of quasi-electrostatic equations which govern the evolution of a 3-D layered piezoelectric body. Assuming that a dissipative effect is effective at the boundary, we study the uniform stabilization problem. We prove that this is indeed the case, provided some geometric conditions on the region and the interfaces hold. We also assume a monotonicity condition on the coefficients. As an application, we deduce exact controllability of the system with boundary control via a classical result due to Russell.

In this paper, we consider the boundary stabilization of asandwich beam which consists of two outer stiff layers and acompliant middle layer. Using Riesz basis approach, we show thatthere is a sequence of generalized eigenfunctions, which forms aRiesz basis in the state space. As a consequence, thespectrum-determined growth condition as well as the exponentialstability of the closed-loop system are concluded. Finally, thewell-posedness and regularity in the sense of Salamon-Weiss classas well as the exact controllability are also addressed.

A model representing the vibrations of a fluid-solid coupled structure is considered. Following Hilbert Uniqueness Method (HUM) introduced by Lions, we establish exact controllability results for this model with an internal controlin the fluid part and there is no control in the solid part. Novel features which arise because of the coupling are pointed out. It is a source of difficulty in the proof of observability inequalities, definition of weak solutions and the proof of controllability results.