Long time behaviour of the solution of Maxwell's equations in dissipative generalized Lorentz materials (I) A frequency dependent Lyapunov function approach - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Zeitschrift für Angewandte Mathematik und Physik Année : 2023

Long time behaviour of the solution of Maxwell's equations in dissipative generalized Lorentz materials (I) A frequency dependent Lyapunov function approach

Résumé

It is well-known that electromagnetic dispersive structures such as metamaterials can be modelled by generalized Drude-Lorentz models. The present paper is the first of two articles dedicated to dissipative generalized Drude-Lorentz open structures. 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 an approach based on frequency dependent Lyapounov estimates, we show that this decay is polynomial in time. These results extend to an unbounded structure the ones obtained for bounded media in [18] via a quite different method based on the notion of cumulated past history and semi-group theory. A great advantage of the approach developed here is to be less abstract and directly connected to the physics of the system via energy balances.
Fichier principal
Vignette du fichier
cassier-joly-rosas-martinez.pdf (682.34 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03850472 , version 1 (13-11-2022)

Licence

Paternité

Identifiants

Citer

Maxence Cassier, Patrick Joly, Luis Alejandro Rosas Martínez. Long time behaviour of the solution of Maxwell's equations in dissipative generalized Lorentz materials (I) A frequency dependent Lyapunov function approach. Zeitschrift für Angewandte Mathematik und Physik, 2023, 74 (3), pp.115. ⟨10.1007/s00033-023-01989-9⟩. ⟨hal-03850472⟩
75 Consultations
43 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More