Simultaneous Exact Control of Quasi-Electrostatic Piezoelectric Systems in Multilayered Media

Abstract

We consider two quasi-electrostatic models in a multilayered piezoelectric structure. Both models only differ on the boundary conditions. For each one of them we prove a boundary observability inequality which together with the Hilbert Uniqueness Method introduced by J.L. Lions allow us to drive both systems to rest at time T with the same control function. We require suitable geometric conditions on the region and the interfaces as well as monotonicity assumptions on the coefficients of the model.