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Journal Articles Mathematical Methods in the Applied Sciences Year : 2003

Solution of axisymmetric Maxwell equations

Franck Assous
Simon Labrunie
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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 H1 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.

Dates and versions

hal-00989564 , version 1 (12-05-2014)

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Franck Assous, Patrick Ciarlet, Simon Labrunie. Solution of axisymmetric Maxwell equations. Mathematical Methods in the Applied Sciences, 2003, 26 (10), pp.861-896. ⟨10.1002/mma.400⟩. ⟨hal-00989564⟩
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