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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2005, Volume 250, Pages 95–104 (Mi tm33)  

This article is cited in 27 scientific papers (total in 27 papers)

Spectral Method in Homogenization Theory

V. V. Zhikov

Vladimir State Pedagogical University
References:
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.
Received in January 2005
Bibliographic databases:
UDC: 517.97
Language: Russian
Citation: V. V. Zhikov, “Spectral Method in Homogenization Theory”, Differential equations and dynamical systems, Collected papers, Trudy 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 Trudy 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://mathscinet.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
Linking options:
  • https://www.mathnet.ru/eng/tm33
  • https://www.mathnet.ru/eng/tm/v250/p95
  • This publication is cited in the following 27 articles:
    1. S. E. Pastukhova, “Error estimates taking account of correctors in homogenization of elliptic operators”, Sb. Math., 215:7 (2024), 932–952  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. I. Y. Popov, E. S. Trifanova, A. S. Bagmutov, I. V. Blinova, “Barrier composed of perforated resonators and boundary conditions”, Eurasian Math. J., 15:3 (2024), 68–76  mathnet  crossref
    3. T. A. Suslina, “Operator-theoretic approach to the homogenization of Schrödinger-type equations with periodic coefficients”, Russian Math. Surveys, 78:6 (2023), 1023–1154  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. D. I. Borisov, “Asymptotic expansion of solution to Dirichlet problem in perforated domain: strange term case”, Ufa Math. J., 14:4 (2022), 26–41  mathnet  crossref
    5. S. E. Pastukhova, “Approximation of resolvents in homogenization of fourth-order elliptic operators”, Sb. Math., 212:1 (2021), 111–134  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. Borisov I D., Cardone G., Chechkin G.A., Koroleva Yu.O., “On Elliptic Operators With Steklov Condition Perturbed By Dirichlet Condition on a Small Part of Boundary”, Calc. Var. Partial Differ. Equ., 60:1 (2021), 48  crossref  mathscinet  isi  scopus
    7. D. I. Borisov, “Asimptoticheskii analiz kraevykh zadach dlya operatora Laplasa s chastoi smenoi tipa granichnykh uslovii”, Differentsialnye uravneniya s chastnymi proizvodnymi, SMFN, 67, no. 1, Rossiiskii universitet druzhby narodov, M., 2021, 14–129  mathnet  crossref
    8. S. E. Pastukhova, “L2L2-approksimatsii rezolventy ellipticheskogo operatora v perforirovannom prostranstve”, Trudy Krymskoi osennei matematicheskoi shkoly-simpoziuma, SMFN, 66, no. 2, Rossiiskii universitet druzhby narodov, M., 2020, 314–334  mathnet  crossref
    9. Pastukhova S.E., “On Resolvent Approximations of Elliptic Differential Operators With Locally Periodic Coefficients”, Lobachevskii J. Math., 41:5, SI (2020), 818–838  crossref  mathscinet  isi  scopus
    10. Pastukhova S.E., “On Resolvent Approximations of Elliptic Differential Operators With Periodic Coefficients”, Appl. Anal., 2020  crossref  mathscinet  isi
    11. Khrabustovskyi A., Post O., “Operator Estimates For the Crushed Ice Problem”, Asymptotic Anal., 110:3-4 (2018), 137–161  crossref  mathscinet  isi
    12. Cardone G., “Waveguides With Fast Oscillating Boundary”, Nanosyst.-Phys. Chem. Math., 8:2 (2017), 160–165  crossref  mathscinet  isi
    13. 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
    14. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    15. S. E. Pastukhova, “Approximation of the Exponential of a Diffusion Operator with Multiscale Coefficients”, Funct. Anal. Appl., 48:3 (2014), 183–197  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    16. 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  crossref  mathscinet  zmath  isi  elib  scopus
    17. S. E. Pastukhova, “Approximations of the operator exponential in a periodic diffusion problem with drift”, Sb. Math., 204:2 (2013), 280–306  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    18. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    19. 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  crossref  mathscinet  isi  elib  scopus
    20. Pastukhova S., “Estimates in homogenization of parabolic equations with locally periodic coefficients”, Asymptot. Anal., 66:3-4 (2010), 207–228  mathscinet  zmath  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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