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 Algebra i Analiz: Year: Volume: Issue: Page: Find

 Algebra i Analiz, 2007, Volume 19, Issue 3, Pages 183–235 (Mi aa124)

Research Papers

Homogenization with corrector for a stationary periodic Maxwell system

T. A. Suslina

St. Petersburg State University, Faculty of Physics

Abstract: The homogenization problem in the small period limit for a stationary periodic Maxwell system in $\mathbb{R}^3$ is studied. It is assumed that the dielectric permittivity and the magnetic permeability are rapidly oscillating (depending on $\mathbf{x}/\varepsilon$), positive definite, and bounded matrix-valued functions. For all four physical fields (the strength of the electric field, the strength of the magnetic field, the electric displacement vector, and the magnetic displacement vector), uniform approximations in the $L_2(\mathbb{R}^3)$-norm are obtained with the (order-sharp) error term of order. Besides solutions of the homogenized Maxwell system, the approximations contain rapidly oscillating terms of zero order that weakly tend to zero. These terms can be interpreted as correctors of zero order.

Keywords: Periodic Maxwell operator, homogenization, effective medium, corrector.

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English version:
St. Petersburg Mathematical Journal, 2008, 19:3, 455–494

Bibliographic databases:

MSC: 35P20, 35Q60

Citation: T. A. Suslina, “Homogenization with corrector for a stationary periodic Maxwell system”, Algebra i Analiz, 19:3 (2007), 183–235; St. Petersburg Math. J., 19:3 (2008), 455–494

Citation in format AMSBIB
\Bibitem{Sus07} \by T.~A.~Suslina \paper Homogenization with corrector for a~stationary periodic Maxwell system \jour Algebra i Analiz \yr 2007 \vol 19 \issue 3 \pages 183--235 \mathnet{http://mi.mathnet.ru/aa124} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2340710} \zmath{https://zbmath.org/?q=an:1202.35319} \transl \jour St. Petersburg Math. J. \yr 2008 \vol 19 \issue 3 \pages 455--494 \crossref{https://doi.org/10.1090/S1061-0022-08-01006-6} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000267653300006} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. M. Sh. Birman, T. A. Suslina, “Operator error estimates in the homogenization problem for nonstationary periodic equations”, St. Petersburg Math. J., 20:6 (2009), 873–928
2. Birman M.S., Suslina T.A., “Homogenization of Periodic Differential Operators as a Spectral Threshold Effect”, New Trends in Mathematical Physics, 2009, 667–683
3. Borisov D., Bunoiu R., Cardone G., “On a waveguide with frequently alternating boundary conditions: homogenized Neumann condition”, Ann. Henri Poincaré, 11:8 (2010), 1591–1627
4. Holloway Ch.L. Kuester E.F., “Corrections to the Classical Continuity Boundary Conditions at the Interface of a Composite Medium”, Photonics Nanostruct., 11:4 (2013), 397–422
5. Borisov D. Cardone G. Durante T., “Homogenization and norm-resolvent convergence for elliptic operators in a strip perforated along a curve”, Proc. R. Soc. Edinb. Sect. A-Math., 146:6 (2016), 1115–1158
6. T. A. Suslina, “Homogenization of a stationary periodic Maxwell system in a bounded domain with constant magnetic permeability”, St. Petersburg Math. J., 30:3 (2019), 515–544
7. Waurick M., “Nonlocal H-Convergence”, Calc. Var. Partial Differ. Equ., 57:6 (2018), 159
8. T. A. Suslina, “Ob usrednenii statsionarnoi periodicheskoi sistemy Maksvella v ogranichennoi oblasti”, Funkts. analiz i ego pril., 53:1 (2019), 88–92
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