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Uniqueness and stability of the solution to a thermoelastic contact problem

Published online by Cambridge University Press:  16 July 2009

Peter Shi  and
Meir Shillor
Peter Shi
Affiliation:
Department of Mathematical Sciences, Oakland University, Rochester, Michigan 48309, USA
Meir Shillor
Affiliation:
Department of Mathematical Sciences, Oakland University, Rochester, Michigan 48309, USA
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Abstract

Uniqueness and continuous dependence on the initial temperature are proved for a onedimensional, quasistatic and frictionless contact problem in linear thermoelasticity. First the problem is reformulated in such a way that it decouples. The resulting problem for the temperature is a nonlinear integro-differential equation. Once the temperature is known the displacement is recovered from an appropriate variational inequality. Uniqueness is proved by considering an integral transform of the temperature. The steady solution is obtained and the asymptotic stability is shown. It turns out that the asymptotic behaviour and the steady state are determined by a relation between the coupling constant a and the initial gap.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 1 , Issue 4 , December 1990 , pp. 371 - 387
Copyright
Copyright © Cambridge University Press 1990

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