Spectral properties of the inhomogeneous Drude-Lorentz model with dissipation

Ferraresso, Francesco ORCID: https://orcid.org/0000-0002-4399-141X and Marletta, Marco ORCID: https://orcid.org/0000-0003-1546-4046 2023. Spectral properties of the inhomogeneous Drude-Lorentz model with dissipation. Journal of Differential Equations 346 , pp. 313-346. 10.1016/j.jde.2022.11.052

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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 θe, θm 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 (ω) 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

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Elsevier
ISSN:	1090-2732
Funders:	EPSRC
Date of First Compliant Deposit:	29 November 2022
Date of Acceptance:	26 November 2022
Last Modified:	05 Jan 2024 05:42
URI:	https://orca.cardiff.ac.uk/id/eprint/154518

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