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

This article is cited in 8 scientific papers (total in 8 papers)

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
Received: 08.02.2007

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
\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
\jour St. Petersburg Math. J.
\yr 2008
\vol 19
\issue 3
\pages 455--494

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    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  mathnet  crossref  mathscinet  zmath  isi
    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  crossref  zmath  isi
    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  crossref  mathscinet  zmath  adsnasa  isi
    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  crossref  adsnasa  isi  elib
    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  crossref  mathscinet  zmath  isi  elib  scopus
    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  mathnet  crossref  mathscinet  isi  elib
    7. Waurick M., “Nonlocal H-Convergence”, Calc. Var. Partial Differ. Equ., 57:6 (2018), 159  crossref  mathscinet  zmath  isi  scopus
    8. T. A. Suslina, “Ob usrednenii statsionarnoi periodicheskoi sistemy Maksvella v ogranichennoi oblasti”, Funkts. analiz i ego pril., 53:1 (2019), 88–92  mathnet  crossref  elib
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