Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-12-01T08:57:08.007Z Has data issue: false hasContentIssue false
  • English
  • Français

A uniqueness result for the thermistor problem

Published online by Cambridge University Press:  16 July 2009

M. Chipot  and
G. Cimatti
M. Chipot
Affiliation:
Département de Mathématiques, Université de Metz, Ile du Saulcy 57045, Metz-Cedex 01, France
G. Cimatti
Affiliation:
Dipartimento di Matematica, Università di Pisa, Via Buonarroti 2, 56100 Pisa, Italy
Get access Rights & Permissions [Opens in a new window]

Abstract

The thermistor problem is a system of equations modelling the electric heating of a conducting material. We prove uniqueness of a solution to this system.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 2 , Issue 2 , June 1991 , pp. 97 - 103
Copyright
Copyright © Cambridge University Press 1991

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Antontseu, S. N. & Chipot, M. 1991 Some results on the thermistor problem (to appear).CrossRefGoogle Scholar
Bensoussan, A. & Lions, J. L. 1982 Applications of Variational Inequalities in Stochastic control. North Holland.Google Scholar
Chipot, M. & Rodrigues, J. F. 1989 On a class of nonlinear nonlocal elliptic problems (to appear in M2AN).Google Scholar
Cimatti, G. 1989a Existence of weak solutions for the nonstationary problem of the Joule heating of a conductor. Preprint, Università di Pisa, Italy.Google Scholar
Cimatti, G. 1988 A bound for the temperature in the thermistor problem. IMA J. Appl. Math. 40, 15–22.CrossRefGoogle Scholar
Cimatti, G. 1989b Remark on existence and uniqueness for the thermistor problem. Quart. J. Appl. Math. 47, 117–121.Google Scholar
Cimatti, G. & Prodi, G. 1989 Existence results for a nonlinear elliptic system modelling a temperature dependent electrical resistor. Ann. Mat. Pura Appl. 152, 227–236.Google Scholar
Diesselhorst, H. 1900 Über das Problem cines elektrisch erwärmten Leiters. Ann. Physics 1, 312–325.CrossRefGoogle Scholar
Fowler, A. C., Frigaard, I. & Howison, S. D. 1991 Temperature surges in current-limiting circuit devices (to appear).Google Scholar
Giaquinta, M. 1983 Multiple Integrals in the calculus of variations and nonlinear elliptic problems. Princeton University Press.Google Scholar
Gilbarg, D. & Trudinger, N. S. 1985 Elliptic Partial Differential Equations of Second order. Springer-Verlag.Google Scholar
Howison, S. D. 1990 A note on the thermistor problem in two space dimensions. Quart. Appl. Math. 47, 509–512.Google Scholar
Kohlrausch, F. 1900 Über den stationären Temperature-zustand eines elektrisch geheizten Leiters. Ann. Physics 1, 132–158.CrossRefGoogle Scholar
Lions, J. L. 1969 Quelques méthodes des résolution des problèmes aux limites non linéaires. Dunod.Google Scholar
Meyers, N. G. 1963 An LP-estimate for the gradient of solution of second order elliptic divergence equations. Ann. Scuola Norm. Sup. Pisa 3, (17), 189–206.Google Scholar