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Existence and regularity results for Maxwell's equations in the quasi-static limit

Published online by Cambridge University Press:  17 February 2009

A. L. Carey  and
D. M. O'Brien
A. L. Carey
Affiliation:
Department of Mathematics, Research School of Physical Sciences, The Australian National University, P.O. Box 4, Canberra 2601.
D. M. O'Brien
Affiliation:
CSIRO Division of Atmospheric Research, Private Bag No. 1, Mordialloc, Victoria.
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Abstract

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We prove the existence of solutions of Maxwell's equations for a conducting medium whose constitutive parameters are piecewise constant on R3, and then examine the convergence of these solutions in the quasi-static limit in which displacement currents are neglected. Secondly, we examine the regularity of the limiting solution and the sense in which the classical boundary conditions hold, namely, continuity of the tangential electric field and the normal current density.

Type
Research Article
Information
The ANZIAM Journal , Volume 27 , Issue 4 , April 1986 , pp. 402 - 415
Copyright
Copyright © Australian Mathematical Society 1986

References

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