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Global solutions of Maxwell's equations in an electromagnetic field with a temperature-dependent electrical conductivity

Published online by Cambridge University Press:  26 September 2008

Hong-Ming Yin
Hong-Ming Yin
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario M5S 1AI, Canada
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Abstract

This paper deals with Maxwell's equations in a quasi-stationary electromagnetic field subject to the effects of temperature. This model is encountered in the penetration of a magnetic field in substances where the electrical conductivity depends on the temperature. Similar phenomena also occur in some industrial problems such as the thermistor. Taking the effect of Joule heating into the consideration, we obtain a strongly coupled nonlinear system. Global solvability is established for this system.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 5 , Issue 1 , March 1994 , pp. 57 - 64
Copyright
Copyright © Cambridge University Press 1994

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References

[1]Chen, X. & Friedman, A. 1991 The thermistor problem for conductivity which vanishes at large temperature. IMA preprint series, No. 792.Google Scholar
[2]Cimatti, G. & Prodi, G. 1988 Existence results for a nonlinear elliptic systems modelling a temperature dependent electrical resistor. Ann. Mat. Pure ed Appl. 152: 227–236.CrossRefGoogle Scholar
[3]Gllbarg, D. & Trudinger, N. 1983 Elliptic Partial Differential Equations of Second Order (2nd ed.). Springer-Verlag.Google Scholar
[4]Landau, L. D. & Lifshitz, E. M. 1960 Electrodynamics of Continuous Media. Pergamon.Google Scholar
[5]Simon, J. 1987 Compact sets in the space Lp(0, T; B). Ann. Mat. Pure ed Appl. 146: 65–96.CrossRefGoogle Scholar
[6]Xie, H. & Allegretto, W. 1991 C α(Ω) solutions of a class of nonlinear degenerate elliptic systems arising in the thermistor problem. SIAM J. Math. Anal. 22: 1491–1499.CrossRefGoogle Scholar
[7]Young, J. M. 1986 Steady state Joule heating with temperature dependent conductivities. Applied Sci. Research 43: 55–65.CrossRefGoogle Scholar
[8]Cimatti, G. 1991 On two problems of electrical heating of conductors. Quart. J. of Appl. Math. XLIX: 729–740.CrossRefGoogle Scholar