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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 

 

Homogenization of a stationary periodic Maxwell system


Author: T. A. Suslina
Translated by: the author
Original publication: Algebra i Analiz, tom 16 (2004), nomer 5.
Journal: St. Petersburg Math. J. 16 (2005), 863-922
MSC (2000): Primary 35P20, 35Q60
DOI: https://doi.org/10.1090/S1061-0022-05-00883-6
Published electronically: September 23, 2005
MathSciNet review: 2106671
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Abstract: The homogenization problem is considered for a stationary periodic Maxwell system in $\mathbb{R} ^3$ in the small period limit. The behavior of four fields is studied, namely, of the strength of the electric field, the strength of the magnetic field, the electric displacement vector, and the magnetic displacement vector. Each field is represented as a sum of two terms. For some terms uniform approximations in the $L_2(\mathbb{R} ^3)$-norm are obtained, together with a precise order estimate for the remainder term.


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Additional Information

T. A. Suslina
Affiliation: Department of Physics, St. Petersburg State University, Ulyanovskaya 1, Petrodvorets, St. Petersburg 198504, Russia
Email: tanya@petrov.stoic.spb.su

DOI: https://doi.org/10.1090/S1061-0022-05-00883-6
Keywords: Periodic Maxwell operator, homogenization, effective medium
Received by editor(s): May 24, 2004
Published electronically: September 23, 2005
Additional Notes: This work was supported by RFBR (grant no. 02-01-00798).
Article copyright: © Copyright 2005 American Mathematical Society