Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-28T02:04:41.711Z Has data issue: false hasContentIssue false
  • English
  • Français

The stationary thermistor problem with a current limiting device

Published online by Cambridge University Press:  14 November 2011

Giovanni Cimatti
Giovanni Cimatti
Affiliation:
Department of Mathematics, University of Pisa, Via Buonarroti 2, 1-56100 Pisa, Italy
Get access Rights & Permissions [Opens in a new window]

Synopsis

The electrical heating of a conductor connected with a current limiting device of total resistance R is studied under mixed boundary conditions. A theorem of existence is given using a transformation which permits the reduction of the nonlinear system governing the problem to the classical mixed boundary value problem for the Laplace equation.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 116 , Issue 1-2 , 1990 , pp. 79 - 84
Copyright
Copyright © Royal Society of Edinburgh 1990

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

1Cimatti, G.. Remark on existence and uniqueness for the thermistor problem under mixed boundary conditions. Quart. Appl. Math. XLVII (1989), 117–121.CrossRefGoogle Scholar
2Kohlrausch, F.. Ueber den stationären Temperature-Zustand eines elektrisch geheizten Leiters. Ann. Phys. 1 (1900), 132–158.CrossRefGoogle Scholar
3Protter, M. H. and Weinberger, H. F.. Maximum principle in partial differential equations (New York: Prentice-Hall, 1967).Google Scholar
4Diesselhorst, H.. Ueber das Probleme eines elektrisch erwärmtern Leiters. Ann. Phys. 1 (1900), 312–325.CrossRefGoogle Scholar
5Fowler, A. C., Howison, S. D. and Hinch, E. J.. Temperature surges in current-limiting circuit devices (to appear).Google Scholar
6Howison, S. D., Rodrigues, J. F. and Shillor, M.. The termistor problem (to appear).Google Scholar