Homogenization of the Stationary Periodic Maxwell System in the Case of Constant Permeability
Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 2, pp. 3-23
Voir la notice de l'article provenant de la source Math-Net.Ru
The homogenization problem in the small period limit for the stationary periodic Maxwell system in $\mathbb{R}^3$ is considered. It is assumed that the permittivity $\eta^\varepsilon(\mathbf{x})=\eta(\varepsilon^{-1}\mathbf{x})}$, $\varepsilon>0$, is a rapidly oscillating positive matrix function and the
permeability $\mu_0$ is a constant positive matrix. For all four physical fields (the
electric and magnetic field intensities, the electric displacement field, and the magnetic flux density), we obtain uniform approximations in the $L_2(\mathbb{R}^3)$-norm with order-sharp remainder estimates.
Keywords:
periodic Maxwell operator, homogenization, effective medium, corrector.
@article{FAA_2007_41_2_a1,
author = {M. Sh. Birman and T. A. Suslina},
title = {Homogenization of the {Stationary} {Periodic} {Maxwell} {System} in the {Case} of {Constant} {Permeability}},
journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
pages = {3--23},
publisher = {mathdoc},
volume = {41},
number = {2},
year = {2007},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FAA_2007_41_2_a1/}
}
TY - JOUR AU - M. Sh. Birman AU - T. A. Suslina TI - Homogenization of the Stationary Periodic Maxwell System in the Case of Constant Permeability JO - Funkcionalʹnyj analiz i ego priloženiâ PY - 2007 SP - 3 EP - 23 VL - 41 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FAA_2007_41_2_a1/ LA - ru ID - FAA_2007_41_2_a1 ER -
%0 Journal Article %A M. Sh. Birman %A T. A. Suslina %T Homogenization of the Stationary Periodic Maxwell System in the Case of Constant Permeability %J Funkcionalʹnyj analiz i ego priloženiâ %D 2007 %P 3-23 %V 41 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/FAA_2007_41_2_a1/ %G ru %F FAA_2007_41_2_a1
M. Sh. Birman; T. A. Suslina. Homogenization of the Stationary Periodic Maxwell System in the Case of Constant Permeability. Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 2, pp. 3-23. http://geodesic.mathdoc.fr/item/FAA_2007_41_2_a1/