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Long time behaviour of the solution of Maxwell's equations in dissipative Lorentz media

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Auteurs : Joly, Patrick (Auteur de la Conférence)
CIRM (Editeur )

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Résumé : In collaboration with Maxence Cassier (Aix Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel) and Luis Alejandro Rosas Martinez (POEMS, CNRS, INRIA, ENSTA Paris).
It is well-known that electromagnetic dispersive structures such as metamaterials obey mathematical models whose construction, based on fundamental physical such as causality and passivity, emphasizes the role of Herglotz functions. Among these models an important class is provided by generalized Drude-Lorentz models, see e.g. [1]. In this work, we are interested in dissipative Drude-Lorentz open structures and we wish to quantify the loss in such media in terms of the long time decay rate of the electromagnetic energy for the corresponding Cauchy problem. By using two different approaches, one based on (frequency dependent) Lyapounov estimates and the other on modal analysis, we show that this decay is polynomial in time. These results generalize a part the ones obtained for bounded media in [2] via a quite different method based on the notion of cumulated past history and semi-group theory. A great advantage of the approaches developed here is to be directly connected to the physics of the system via energy balances or modes behavior.

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    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 20/06/2022
    Date de captation : 25/05/2022
    Sous collection : Research talks
    arXiv category : Analysis of PDEs ; Numerical Analysis
    Domaine : Numerical Analysis & Scientific Computing ; Mathematical Physics
    Format : MP4 (.mp4) - HD
    Durée : 00:58:04
    Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2022-05-25_Joly.mp4

Informations sur la Rencontre

Nom de la rencontre : Herglotz-Nevanlinna Functions and their Applications to Dispersive Systems and Composite Materials / Fonctions de Herglotz-Nevanlinna et leurs applications aux systèmes dispersifs et aux matériaux composites
Organisateurs de la rencontre : Bonnet-Ben Dhia, Anne-Sophie ; Cassier, Maxence ; Gralak, Boris ; Luger, Annemarie ; Milton, Graeme
Dates : 23/05/2022 - 27/05/2022
Année de la rencontre : 2022
URL Congrès : https://conferences.cirm-math.fr/2225.html

Données de citation

DOI : 10.24350/CIRM.V.19919903
Citer cette vidéo: Joly, Patrick (2022). Long time behaviour of the solution of Maxwell's equations in dissipative Lorentz media. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19919903
URI : http://dx.doi.org/10.24350/CIRM.V.19919903

Voir aussi

Bibliographie

  • CASSIER, Maxence, JOLY, Patrick, et KACHANOVSKA, Maryna. Mathematical models for dispersive electromagnetic waves: an overview. Computers & Mathematics with Applications, 2017, vol. 74, no 11, p. 2792-2830. - https://doi.org/10.1016/j.camwa.2017.07.025

  • NICAISE, Serge et PIGNOTTI, Cristina. Asymptotic behavior of dispersive electromagnetic waves in bounded domains. Zeitschrift für angewandte Mathematik und Physik, 2020, vol. 71, no 3, p. 1-26. - http://dx.doi.org/10.1007/s00033-020-01297-6



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