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Mathematical models for dispersive electromagnetic waves: An overview

Maxence Cassier 1 Patrick Joly 2 Maryna Kachanovska 2
2 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
CNRS - Centre National de la Recherche Scientifique : UMR7231, UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France
Abstract : In this work, we investigate mathematical models for electromagnetic wave propagation in dispersive isotropic media. We emphasize the link between physical requirements and mathematical properties of the models. A particular attention is devoted to the notion of non-dissipativity and passivity. We consider successively the case of so-called local media and general passive media. The models are studied through energy techniques, spectral theory and dispersion analysis of plane waves. For making the article self-contained, we provide in appendix some useful mathematical background.
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Submitted on : Friday, November 24, 2017 - 12:01:59 PM
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Maxence Cassier, Patrick Joly, Maryna Kachanovska. Mathematical models for dispersive electromagnetic waves: An overview. Computers & Mathematics with Applications, Elsevier, 2017, 74 (11), pp.2792-2830. ⟨10.1016/j.camwa.2017.07.025⟩. ⟨hal-01647185⟩

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