Stabilization of a layered piezoelectric 3-D body by boundary dissipation
Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Russia, Visiting Researcher at the National Laboratory of Scientific Computation (LNCC/MCT), Brasil; firstname.lastname@example.org
2 Laboratoire de Modélisation et Simulation numérique, École Supérieure d'Ingénieurs en Électrotechnique et Électronique, 2 Boulevard Blaise Pascal, 93160 Noisy-le-Grand, France; email@example.com
3 National Laboratory of Scientific Computation LNCC/MCT, Rua Getulio Vargas 333, Quitandinha, Petropolis 25651-070, RJ, Brasil and Institute of Mathematics Federal University of Rio de Janeiro, RJ, P.O. 68530, Rio de Janeiro, RJ, Brasil; firstname.lastname@example.org
Revised: 4 January 2005
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.
Mathematics Subject Classification: 35Q99 / 74F99 / 35B40
Key words: Distributed systems / boundary control / stabilization / exact controllability.
© EDP Sciences, SMAI, 2006