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Stabilization of a layered piezoelectric 3-D body by boundary dissipation

Published online by Cambridge University Press:  22 March 2006

Boris Kapitonov ,
Bernadette Miara  and
Gustavo Perla Menzala
Boris Kapitonov
Affiliation:
Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Russia, Visiting Researcher at the National Laboratory of Scientific Computation (LNCC/MCT), Brasil; borisvk@lncc.br
Bernadette Miara
Affiliation:
Laboratoire de Modélisation et Simulation numérique, École Supérieure d'Ingénieurs en Électrotechnique et Électronique, 2 Boulevard Blaise Pascal, 93160 Noisy-le-Grand, France; miarab@esiee.fr
Gustavo Perla Menzala
Affiliation:
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; perla@lncc.br
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Abstract

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.

Keywords

Distributed systemsboundary controlstabilizationexact controllability.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 12 , Issue 2 , April 2006 , pp. 198 - 215
Copyright
© EDP Sciences, SMAI, 2006

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