@article{Nicaise2025, 
author = {Serge Nicaise and Roland Schnaubelt},
title = {Maxwell equations with localized internal damping: strong and polynomial stability},
year = {2025},
journal = {Communications in Analysis and Mechanics},
volume = {17},
number = {4},
pages = {849-877},
keywords = {stability, Maxwell system, localized conductivity, ABLV theorem, Borichev–Tomilov theorem},
url = {https://www.sciopen.com/article/10.3934/cam.2025034},
doi = {10.3934/cam.2025034},
abstract = {We study the Maxwell system with localized conductivity    σ and the boundary conditions of a perfect conductor on a simply connected domain    Ω, assuming that there are no electric charges off the support of    σ. For matrix-valued permittivity    ε and permeability    μ, we show strong stability of the underlying semigroup by checking the spectral criteria of the Arendt–Batty–Lyubich–Vũ Theorem. If    ε  =  μ  =  1,    Ω is the cube    (  0  ,  π      )    3   and    supp    σ contains a strip, the semigroup is polynomially stable of rate        1    2  . To derive this result, we establish the resolvent estimate of the Borichev–Tomilov Theorem using an orthonormal basis of eigenfunctions of the Maxwell operator for    σ  =  0.}
}