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Solution of axisymmetric Maxwell equations

✍ Scribed by Franck Assous; Patrick Ciarlet Jr; Simon Labrunie

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
309 KB
Volume
26
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

In this article, we study the static and time‐dependent Maxwell equations in axisymmetric geometry. Using the mathematical tools introduced in (Math. Meth. Appl. Sci. 2002; 25: 49), we investigate the decoupled problems induced in a meridian half‐plane, and the splitting of the solution in a regular part and a singular part, the former being in the Sobolev space H^1^ component‐wise. It is proven that the singular parts are related to singularities of Laplace‐like or wave‐like operators. We infer from these characterizations: (i) the finite dimension of the space of singular fields; (ii) global space and space–time regularity results for the electromagnetic field. This paper is the continuation of (Modél. Math. Anal. Numér. 1998; 32: 359, Math. Meth. Appl. Sci. 2002; 25: 49). Copyright © 2003 John Wiley & Sons, Ltd.

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