European Journal of Applied Mathematics

Research Article

Uniqueness and stability of the solution to a thermoelastic contact problem

Peter Shia1 and Meir Shillora1

a1 Department of Mathematical Sciences, Oakland University, Rochester, Michigan 48309, USA

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.

(Received July 20 1990)