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On the time-asymptotic behaviour of solutions in thermoelasticity*

Published online by Cambridge University Press:  14 November 2011

Reinhard Racke
Reinhard Racke
Affiliation:
Institut für Angewandte Mathematik der Universität Bonn, Wegelerstrasse 10, D-5300 Bonn 1, Federal Republic of, Germany
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Synopsis

We consider initial boundary value problems for the equations of linear thermoelasticity in both bounded and unbounded domains and for both nonhomogeneous and anisotropic media. For bounded domains, it is shown that the unique solution of the problem is time-asymptotically equal to the solution of a particular initial boundary value problem which is obtained from a natural decomposition of the original initial data and which represents a (in general non-vanishing) time harmonic part. For the unbounded case similar results are obtained, but now in the sense of weak convergence which lead to the result of local energy decay: the solution tends to zero in every compactum.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 107 , Issue 3-4 , 1987 , pp. 289 - 298
Copyright
Copyright © Royal Society of Edinburgh 1987

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