Essential spectrum for Maxwell's equations

Alberti, Giovanni S., Brown, Malcolm ORCID: https://orcid.org/0000-0002-2871-6591, Marletta, Marco ORCID: https://orcid.org/0000-0003-1546-4046 and Wood, Ian 2019. Essential spectrum for Maxwell's equations. Annales Henri Poincaré 20 , pp. 1471-1499. 10.1007/s00023-019-00762-x

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Abstract

We study the essential spectrum of operator pencils associated with anisotropic Maxwell equations, with permittivity ε , permeability μ and conductivity σ , on finitely connected unbounded domains. The main result is that the essential spectrum of the Maxwell pencil is the union of two sets: namely, the spectrum of the pencil div((ωε+iσ)∇⋅) , and the essential spectrum of the Maxwell pencil with constant coefficients. We expect the analysis to be of more general interest and to open avenues to investigation of other questions concerning Maxwell’s and related systems.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics Computer Science & Informatics
Subjects:	Q Science > QA Mathematics
Additional Information:	This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Publisher:	Springer
ISSN:	1424-0637
Funders:	EPSRC
Date of First Compliant Deposit:	17 January 2019
Date of Acceptance:	27 December 2018
Last Modified:	05 May 2023 12:02
URI:	https://orca.cardiff.ac.uk/id/eprint/118080

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