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
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  2. 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.
  3. 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.
  4. 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.
  5. 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.
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  7. 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.
  8. T. Kato. Perturbation theory for linear operators, 2nd ed. Grundlehren Math. Wiss., vol. 132, Springer-Verlag, Berlin-New York, 1976.
  9. E. Sanchez-Palencia. Nonhomogeneous media and vibration theory. Lecture Notes in Phys., vol. 127, Springer-Verlag, Berlin–New York, 1980.
  10. 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.
  11. T. A. Suslina. Homogenization of periodic parabolic Cauchy problem. Amer. Math. Soc. Transl., ser. 2, 220 (2007), 201–233.
  12. 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.
  13. 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.
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  16. 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.

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