We establish spectral enclosures and spectral approximation results for the inhomogeneous lossy Drude-Lorentz system with purely imaginary poles, in a possibly unbounded Lipschitz domain of R3. Under the assumption that the coefficients theta e, theta m of the material are asymptotically constant at infinity, we prove that spectral pollution due to domain truncation can lie only in the essential numerical range of a curl curl0 -f (omega) pencil.As an application, we consider a conducting metamaterial at the interface with the vacuum; we prove that the complex eigenvalues with non-trivial real part lie outside the set of spectral pollution. We believe this is the first result of enclosure of spectral pollution for the Drude-Lorentz model without assumptions of compactness on the resolvent of the underlying Maxwell operator.(c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Spectral properties of the inhomogeneous Drude-Lorentz model with dissipation / Ferraresso, F; Marletta, M. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 346:(2023), pp. 313-346. [10.1016/j.jde.2022.11.052]

Spectral properties of the inhomogeneous Drude-Lorentz model with dissipation

Ferraresso, F
;
2023-01-01

Abstract

We establish spectral enclosures and spectral approximation results for the inhomogeneous lossy Drude-Lorentz system with purely imaginary poles, in a possibly unbounded Lipschitz domain of R3. Under the assumption that the coefficients theta e, theta m of the material are asymptotically constant at infinity, we prove that spectral pollution due to domain truncation can lie only in the essential numerical range of a curl curl0 -f (omega) pencil.As an application, we consider a conducting metamaterial at the interface with the vacuum; we prove that the complex eigenvalues with non-trivial real part lie outside the set of spectral pollution. We believe this is the first result of enclosure of spectral pollution for the Drude-Lorentz model without assumptions of compactness on the resolvent of the underlying Maxwell operator.(c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
2023
Spectral properties of the inhomogeneous Drude-Lorentz model with dissipation / Ferraresso, F; Marletta, M. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 346:(2023), pp. 313-346. [10.1016/j.jde.2022.11.052]
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11388/307010
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 2
social impact