Free Access
Issue |
Math. Model. Nat. Phenom.
Volume 5, Number 4, 2010
Spectral problems. Issue dedicated to the memory of M. Birman
|
|
---|---|---|
Page(s) | 390 - 447 | |
DOI | https://doi.org/10.1051/mmnp/20105416 | |
Published online | 12 May 2010 |
- N. S. Bakhvalov, 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. Publishers Group, Dordrecht, 1989. [Google Scholar]
- A. Bensoussan, J. L. Lions, G. Papanicolaou. Asymptotic analysis for periodic structures. Stud. Math. Appl., vol. 5, North-Holland Publishing Company, Amsterdam–New York, 1978, 700 pp. [Google Scholar]
- M. Birman, T. Suslina. Threshold effects near the lower edge of the spectrum for periodic differential operators of mathematical physics. Systems, Approximation, Singular Integral Operators, and Related Topics (Bordeaux, 2000), Oper. Theory Adv. Appl., vol. 129, Birkhäuser, Basel, 2001, pp. 71–107. [Google Scholar]
- M. Sh. Birman, T. A. Suslina. 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. [Google Scholar]
- M. Sh. Birman, T. A. Suslina. Threshold approximations with corrector term for the resolvent of a factorized selfadjoint operator family. Algebra i Analiz, 17 (2005), no. 5, 69–90; English transl., St. Petersburg Math. J.,17 (2006), no. 5, 745–762. [Google Scholar]
- M. Sh. Birman, T. A. Suslina. Homogenization with corrector term for periodic elliptic differential operators, Algebra i Analiz, 17 (2005), no. 6, 1–104. [Google Scholar]
- M. Sh. Birman, T. A. Suslina. Homogenization with corrector for periodic differential operators. Approximation of solutions in the Sobolev classH1(d), Algebra i Analiz, 18 (2006), no. 6, 1–130; English transl., St. Petersburg Math. J., 18 (2007), no. 6, 857–955. [Google Scholar]
- T. Kato. Perturbation theory for linear operators, 2nd ed. Grundlehren Math. Wiss., vol. 132, Springer-Verlag, Berlin-New York, 1976. [Google Scholar]
- E. Sanchez-Palencia. Nonhomogeneous media and vibration theory. Lecture Notes in Phys., vol. 127, Springer-Verlag, Berlin–New York, 1980. [Google Scholar]
- T. A. Suslina. Homogenization of periodic parabolic systems. Funktsional. Anal. i Prilozhen., 38 (2004), no. 4, 86-90; English transl., Funct. Anal. Appl.,38 (2004), no. 4, 309–312. [Google Scholar]
- T. A. Suslina. Homogenization of periodic parabolic Cauchy problem. Amer. Math. Soc. Transl., ser. 2, 220 (2007), 201–233. [Google Scholar]
- E. S. Vasilevskaya. A periodic parabolic Cauchy problem: homogenization with corrector. Algebra i Analiz, 20 (2009), no. 1, 3–60; English transl., St. Petersburg Math. J., 20 (2010), no. 1. [Google Scholar]
- V. V. Zhikov, On some estimates of homogenization theory. Dokl. Ros. Akad. Nauk, 406 (2006), no. 5, 597–601; English transl., Dokl. Math., 73 (2006), 96–99. [Google Scholar]
- V. V. Zhikov, S. M. Kozlov, O. A. Oleinik. Homogenization of differential operators. "Nauka", Moscow, 1993; English transl., Springer-Verlag, Berlin, 1994. [Google Scholar]
- V. V. Zhikov, S. E. Pastukhova. On operator estimates for some problems in homogenization theory. Russ. J. Math. Phys., 12 (2005), no. 4, 515–524. [MathSciNet] [Google Scholar]
- V. V. Zhikov, S. E. Pastukhova. Estimates of homogenization for a parabolic equation with periodic coefficients. Russ. J. Math. Phys., 13 (2006), no. 2, 251–265. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.