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IMA Journal of Applied Mathematics Advance Access published online on August 24, 2009
IMA Journal of Applied Mathematics, doi:10.1093/imamat/hxp022
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© The Author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

The transmission problem to thermoelastic plate of hyperbolic type

Juan C. Vila Bravo{dagger}

Federal University of Parana, PO Box 019081, Curitiba CEP 81531-990, Parana, Brazil

Jaime E. Muñoz Rivera

National Laboratory for Scientific Computation, Rua Getulio Vargas 333, CEP 25651-070 Rio de Janeiro, Brazil

{dagger} Email: jcvb{at}mat.ufpr.br

Received on November 12, 2008; Revision received July 1, 2009. Accepted on July 3, 2009

In this paper, we consider the thermoelastic plate equations with localized thermal dissipation of memory type, proposed by Gurtin & Pipkin (1968, Arch. Ration. Mech. Anal., 31, 113–126). We will show that the solution of the corresponding model decays exponentially as time goes to infinity, provided the relaxation function decays exponentially. The main difference between the current model and other thermoelastic systems is that the whole system is of hyperbolic type and the ‘dissipation’ is weaker (indefinite) than that given by the Fourier law for the heat flux.

Keywords: exponential stability; transmission problem; thermoelasticity.


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