Essential spectrum for dissipative Maxwell equations in domains with cylindrical ends

We consider the Maxwell equations with anisotropic coefficients and non -trivial conductivity in a domain with finitely many cylindrical ends. We assume that the conductivity vanishes at infinity and that the permittivity and permeability tensors converge to non -constant matrices at infinity, which coincide with a positive real multiple of the identity matrix in each of the cylindrical ends. We establish that the essential spectrum of Maxwell system can be decomposed as the union of the essential spectrum of a bounded multiplication operator acting on gradient fields, and the union of the essential spectra of the Maxwell systems obtained by freezing the coefficients to their different limiting values along the several different cylindrical ends of the domain. (c) 2024 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/).