PORTUGALIAEMATHEMATICA
Vol. 60, No. 4, pp. 411-454 (2003)
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PORTUGALIAE MATHEMATICA Vol. 60, No. 4, pp. 411-454 (2003) |
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Uniform Stabilization and Exact Control of a Multilayered Piezoelectric BodyBoris V. Kapitonov and G. Perla MenzalaSobolev Institute of Mathematics,Siberian Branch of Russian Academy of Sciences -- RUSSIA E-mail: borisvk@lncc.br National Laboratory of Scientific Computation LNCC/MCT, Rua Getulio Vargas 333, Quitandinha, Petropolis, 25651-070, RJ -- BRASIL and Federal University of Rio de Janeiro, Institute of Mathematics, P.O. Box 68530, 21945-970, Rio de Janeiro, RJ -- BRASIL E-mail: perla@lncc.br Abstract: A transmission problem for a class of dynamic coupled system of hyperbolic equations having piecewise constant coefficients in a bounded three-dimensional domain is considered. Assuming that in the entire boundary, dissipative mechanisms are present and that suitable geometric conditions on the domain and the interfaces are satisfied, we prove that the total energy associated with the model decays exponentially as $t\to+\infty$. Exact boundary controllability is then obtained through Russell's controllability via stabilizability principle. Keywords: uniform stabilization; transmission problem; piezoelectric body. Classification (MSC2000): 35Q99, 35Q60, 35L99. Full text of the article:
Electronic version published on: 9 Feb 2006. This page was last modified: 27 Nov 2007.
© 2003 Sociedade Portuguesa de Matemática
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