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IMA Journal of Applied Mathematics Advance Access published online on April 29, 2009
IMA Journal of Applied Mathematics, doi:10.1093/imamat/hxp020
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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.

Energy decay in a transmission problem in thermoelasticity of type III

Salim A. Messaoudi{dagger}

Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Belkacem Said-Houari{ddagger}

Institut de Mathématiques de Toulouse, Mathématiques pour lIndustrie et la Physique, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 09, France
Université Badji Mokhtar, Département de Mathématiques B.P. 12 Annaba 23000. Algerie

{dagger} Email: messaoud{at}kfupm.edu.sa

{ddagger} Email: saidhouarib{at}yahoo.fr

Received on April 11, 2007; Accepted on March 14, 2009

In this paper, we consider a 1D linear thermoelastic transmission problem, where the heat conduction is described by the theories of Green and Naghdi. By using the energy method, we prove that the thermal effect is strong enough to produce an exponential stability of the solution, no matter how small the action domain is.

Keywords: thermoelasticity; energy decay; transmission problem.


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