A thermo piezoelectric model: Exponential decay of the total energy

Gustavo Alberto Perla Menzala; Julian Moises Sejje Suárez

doi:10.3934/dcds.2013.33.5273

Article Contents

2013, Volume 33, Issue 11&12: 5273-5292. Doi: 10.3934/dcds.2013.33.5273

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A thermo piezoelectric model: Exponential decay of the total energy

1.
National Laboratory of Scientific Computation, LNCC/MCT, Av. Getulio Vargas 333, Quitandinha, Petrópolis, RJ, 25651-070
2.
National Laboratory of Scientific Computation, LNCC/MCT, Av. Getulio Vargas 333, Quitandinha, Petrópolis, RJ, CEP 25651-070

Received: September 30, 2011

Revised: March 31, 2012

Published: October 2013

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Abstract

We consider a linear evolution model describing a piezoelectric phenomenon under thermal effects as suggested by R. Mindlin [13] and W. Nowacki [16]. We prove the equivalence between exponential decay of the total energy and an observability inequality for an anisotropic elastic wave system. Our strategy is to use a decoupling method to reduce the problem to an equivalent observability inequality for an anisotropic elastic wave system and assume a condition which guarantees that the corresponding elliptic operator has no eigenfunctions with null divergence.

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Mathematics Subject Classification: 35B40, 74H40.

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