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Homogenization of a stationary periodic Maxwell system
Author(s):
T.
A.
Suslina
Translated by:
the author
Original publication:
Algebra i Analiz,
tom 16
(2004),
vypusk 5.
Journal:
St. Petersburg Math. J.
16
(2005),
863-922.
MSC (2000):
Primary 35P20, 35Q60
Posted:
September 23, 2005
MathSciNet review:
2106671
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References |
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Abstract:
The homogenization problem is considered for a stationary periodic Maxwell system in  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  -norm are obtained, together with a precise order estimate for the remainder term.
References:
-
- [BaPa]
- N. S. Bakhvalov and G. P. Panasenko, Homogenization: averaging processes in periodic media. Mathematical problems in the mechanics of composite materials, ``Nauka'', Moscow, 1984; English transl., Math. Appl. (Soviet Ser.), vol. 36, Kluwer Acad. Publ. Group, Dordrecht, 1989. MR 0797571 (86m:73049); MR 1112788 (92d:73002)
- [BeLP]
- A. Bensoussan, J.-L. Lions, and G. Papanicolaou, Asymptotic analysis for periodic structures, Stud. Math. Appl., vol. 5, North-Holland Publishing Co., Amsterdam-New York, 1978. MR 0503330 (82h:35001)
- [BS1]
- M. Sh. Birman and M. Z. Solomyak, The self-adjoint Maxwell operator in arbitrary domains, Algebra i Analiz 1 (1989), vyp. 1, 96-110; English transl., Leningrad Math. J. 1 (1990), no. 1, 99-115. MR 1015335 (91e:35197)
- [BS2]
- -, Schrödinger operator. Estimates for number of bound states as function-theoretical problem, Amer. Math. Soc. Transl. Ser. 2, vol. 150, Amer. Math. Soc., Providence, RI, 1992, pp. 1-54. MR 1157648 (93j:35120)
- [BSu1]
- M. Sh. Birman and T. A. Suslina, Threshold effects near the lower edge of the spectrum for periodic differential operators of mathematical physics, Systems, Approximations, Singular Integral Operators and Related Topics (Bordeaux, 2000), Oper. Theory Adv. Appl., vol. 129, Birkhäuser, Basel, 2001, pp. 71-107. MR 1882692 (2003f:35220)
- [BSu2]
- -, Second order periodic differential operators. Threshold properties and homogenization, Algebra i Analiz 15 (2003), no. 5, 1-108; English transl., St. Petersburg Math. J. 15 (2004), no. 5, 639-714. MR 2068790
- [ZhKO]
- V. V. Zhikov, S. M. Kozlov, and O. A. Oleinik, Homogenization of differential operators, ``Nauka'', Moscow, 1993; English transl., Springer-Verlag, Berlin, 1994. MR 1318242 (96h:35003a); MR 1329546 (96h:35003b)
- [LU]
- O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and quasilinear equations of the elliptic type, ``Nauka'', Moscow, 1964; English transl., Acad. Press, New York-London, 1968. MR 0211073 (35:1955); MR 0244627 (39:5941)
- [Sa]
- E. Sanchez-Palencia, Nonhomogeneous media and vibration theory, Lecture Notes in Phys., vol. 127, Springer-Verlag, Berlin-New York, 1980. MR 0578345 (82j:35010)
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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:
10.1090/S1061-0022-05-00883-6
PII:
S 1061-0022(05)00883-6
Keywords:
Periodic Maxwell operator,
homogenization,
effective medium
Received by editor(s):
24/MAY/2004
Posted:
September 23, 2005
Additional Notes:
This work was supported by RFBR (grant no. 02-01-00798).
Copyright of article:
Copyright
2005,
American Mathematical Society
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