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 Tr. Mat. Inst. Steklova, 2005, Volume 250, Pages 95–104 (Mi tm33)

This article is cited in 17 scientific papers (total in 17 papers)

Spectral Method in Homogenization Theory

V. V. Zhikov

Vladimir State Pedagogical University

Abstract: The problem of homogenization (in the whole space) is considered. The so-called spectral method is applied in order to estimate the difference between the exact solution and special approximations.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2005, 250, 85–94

Bibliographic databases:
UDC: 517.97
Received in January 2005

Citation: V. V. Zhikov, “Spectral Method in Homogenization Theory”, Differential equations and dynamical systems, Collected papers, Tr. Mat. Inst. Steklova, 250, Nauka, MAIK «Nauka/Inteperiodika», M., 2005, 95–104; Proc. Steklov Inst. Math., 250 (2005), 85–94

Citation in format AMSBIB
\Bibitem{Zhi05} \by V.~V.~Zhikov \paper Spectral Method in Homogenization Theory \inbook Differential equations and dynamical systems \bookinfo Collected papers \serial Tr. Mat. Inst. Steklova \yr 2005 \vol 250 \pages 95--104 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm33} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2200910} \zmath{https://zbmath.org/?q=an:1127.35311} \transl \jour Proc. Steklov Inst. Math. \yr 2005 \vol 250 \pages 85--94 

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This publication is cited in the following articles:
1. M. Sh. Birman, T. A. Suslina, “Averaging of periodic elliptic differential operators with the account of a corrector”, St. Petersburg Math. J., 17:6 (2006), 897–973
2. Zhikov V.V., Pastukhova S.E., “On operator estimates for some problems in homogenization theory”, Russ. J. Math. Phys., 12:4 (2005), 515–524
3. S. A. Nazarov, “Homogenization of elliptic systems with periodic coefficients: Weighted $L^p$ and $L^\infty$ estimates for asymptotic remainders”, St. Petersburg Math. J., 18:2 (2007), 269–304
4. Kamotski V., Matthies K., Smyshlyaev V.P., “Exponential homogenization of linear second order elliptic PDEs with periodic coefficients”, SIAM J. Math. Anal., 38:5 (2006), 1565–1587
5. V. V. Zhikov, S. E. Pastukhova, “Homogenization of degenerate elliptic equations”, Siberian Math. J., 49:1 (2008), 80–101
6. S. E. Pastukhova, “Operator Estimates in Nonlinear Problems of Reiterated Homogenization”, Proc. Steklov Inst. Math., 261 (2008), 214–228
7. G. Cardone, A. Corbo Esposito, S. A. Nazarov, “Homogenization of the mixed boundary value problem for a formally self-adjoint system in a periodically perforated domain”, St. Petersburg Math. J., 21:4 (2010), 601–634
8. Pastukhova S., “Estimates in homogenization of parabolic equations with locally periodic coefficients”, Asymptot. Anal., 66:3-4 (2010), 207–228
9. Andrianov I.V., Awrejcewicz J., Danishevs'kyy V.V., Weichert D., “Wave Propagation in Periodic Composites: Higher-Order Asymptotic Analysis Versus Plane-Wave Expansions Method”, J. Comput. Nonlinear Dynam., 6:1 (2011), 011015
10. S. E. Pastukhova, “Approximations of the operator exponential in a periodic diffusion problem with drift”, Sb. Math., 204:2 (2013), 280–306
11. S. E. Pastukhova, “Approximations of the Resolvent for a Non–Self-Adjoint Diffusion Operator with Rapidly Oscillating Coefficients”, Math. Notes, 94:1 (2013), 127–145
12. T. F. Sharapov, “On the resolvent of multidimensional operators with frequently changing boundary conditions in the case of the homogenized Dirichlet condition”, Sb. Math., 205:10 (2014), 1492–1527
13. S. E. Pastukhova, “Approximation of the Exponential of a Diffusion Operator with Multiscale Coefficients”, Funct. Anal. Appl., 48:3 (2014), 183–197
14. Borisov D., Cardone G., Durante T., “Norm-Resolvent Convergence For Elliptic Operators in Domain With Perforation Along Curve”, C. R. Math., 352:9 (2014), 679–683
15. 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
16. Cardone G., “Waveguides With Fast Oscillating Boundary”, Nanosyst.-Phys. Chem. Math., 8:2 (2017), 160–165
17. Khrabustovskyi A., Post O., “Operator Estimates For the Crushed Ice Problem”, Asymptotic Anal., 110:3-4 (2018), 137–161
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