Abstract
Uniqueness and continuous dependence on the initial temperature are established for the solution of a multidimensional, quasistatic thermoelastic contact problem. The proof of this result does not depend on the ability to decouple the system of governing equations as required in the technique used by Shi and Shillor [European J. Appl. Math., 1990, 371–387] in the one dimensional analogue of this problem. Some extensions to other contact problems are suggested.
Similar content being viewed by others
References
K.T.Andrews, A.Mikelić, P.Shi, M.Shillor and S.Wright, One-dimensional thermoelastic contact with a stress-dependent radiation condition.SIAM J. Math. Anal. 23 (1992) 1393–1416.
K.T. Andrews, P. Shi, M. Shillor and S. Wright, Thermoelastic contact with Barber's heat exchange condition, to appear inApplied Math. Optimization.
M.I.M. Copetti and C.M. Elliot, A one dimensional quasi-static contact problem in linear thermoelasticity, preprint.
W.A.Day, Justification of the uncoupled and quasistatic approximations in a problem of dynamic thermoelasticity.Arch. Rat. Mech. Anal. 80 (1988) 135–158.
G. Duvaut, Free boundary problems connected with thermoelasticity and unilateral contact.Free Boundary Problems Vol. II, Roma (1980).
G.Duvaut and J. L.Lions, Théquations en thermoélasticité et magnétohydrodynamique.Arch. Rat. Mech. Anal. 46 (1972) 241–279.
R.P.Gilbert, P.Shi, and M.Shillor, A quasistatic contact problem in linear thermoelasticity.Rendiconti di Mat. 10 (1990) 785–808.
P.Shi and M.Shillor, Uniqueness and stability of the solution to a thermoelastic contact problem.European J. Appl. Math. 1 (1990) 371–387.
P. Shi and M. Shillor, A quasistatic contact problem in thermoelasticity with a radiation condition for the temperature, to appear inJ. Math. Anal. App.
P.Shi and M.Shillor, Existence of a solution to then dimensional problem of thermoelastic contact.Comm. P.D.E. 17 (1992) 1597–1618.
P.Shi, M.Shillor and X.Zou, Numerical solutions to one dimensional problems of thermoelastic contact.Computers Math. Applic. 22 (1991) 65–78.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ames, K.A., Payne, L.E. Uniqueness and continuous dependence of solutions to a multidimensional thermoelastic contact problem. J Elasticity 34, 139–148 (1994). https://doi.org/10.1007/BF00041189
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00041189