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Uspekhi Mat. Nauk, 2002, Volume 57, Issue 4(346), Pages 75–94 (Mi umn534)  

This article is cited in 23 scientific papers (total in 23 papers)

Quantitative homogenization of global attractors for hyperbolic wave equations with rapidly oscillating coefficients

B. Fiedlera, M. I. Vishikb

a Freie Universität Berlin
b Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: The rate of convergence of solutions and attractors to the corresponding solutions and attractors of the limit homogenized equation is estimated.


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English version:
Russian Mathematical Surveys, 2002, 57:4, 709–728

Bibliographic databases:

UDC: 517.95
MSC: Primary 35L70, 35L05, 35B41; Secondary 35B27, 35L90, 37B25
Received: 05.04.2002

Citation: B. Fiedler, M. I. Vishik, “Quantitative homogenization of global attractors for hyperbolic wave equations with rapidly oscillating coefficients”, Uspekhi Mat. Nauk, 57:4(346) (2002), 75–94; Russian Math. Surveys, 57:4 (2002), 709–728

Citation in format AMSBIB
\by B.~Fiedler, M.~I.~Vishik
\paper Quantitative homogenization of global attractors for hyperbolic wave equations with rapidly oscillating coefficients
\jour Uspekhi Mat. Nauk
\yr 2002
\vol 57
\issue 4(346)
\pages 75--94
\jour Russian Math. Surveys
\yr 2002
\vol 57
\issue 4
\pages 709--728

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    This publication is cited in the following articles:
    1. Fiedler B., Vishik M.I., “Quantitative homogenization of global attractors for reaction-diffusion systems with rapidly oscillating terms”, Asymptot. Anal., 34:2 (2003), 159–185  mathscinet  zmath  isi  elib
    2. M. I. Vishik, V. V. Chepyzhov, “Approximation of trajectories lying on a global attractor of a hyperbolic equation with exterior force rapidly oscillating in time”, Sb. Math., 194:9 (2003), 1273–1300  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Chepyzhov V.V., Goritsky A.Yu., Vishik M.I., “Integral manifolds and attractors with exponential rate for nonautonomous hyperbolic equations with dissipation”, Russ. J. Math. Phys., 12:1 (2005), 17–39  mathscinet  zmath  isi  elib
    4. Chepyzhov V.V., Vishik M.I., Wendland W.L., “On non-autonomous sine-Gordon type equations with a simple global attractor and some averaging”, Discrete Contin. Dyn. Syst., 12:1 (2005), 27–38  crossref  mathscinet  zmath  isi  elib
    5. M. I. Vishik, V. V. Chepyzhov, “Attractors of dissipative hyperbolic equations with singularly oscillating external forces”, Math. Notes, 79:4 (2006), 483–504  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. Zelik S., “Global averaging and parametric resonances in damped semilinear wave equations”, Proc. Roy. Soc. Edinburgh Sect. A, 136:5 (2006), 1053–1097  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    7. Cavalcanti M.M., Domingos Cavalcanti V.N., Andrade D., Ma T.F., “Homogenization for a nonlinear wave equation in domains with holes of small capacity”, Discrete Contin. Dyn. Syst., 16:4 (2006), 721  crossref  mathscinet  zmath  isi  elib
    8. M. I. Vishik, V. V. Chepyzhov, “The global attractor of the nonautonomous 2D Navier–Stokes system with singularly oscillating external force”, Dokl. Math., 75:2 (2007), 236  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    9. Yu. A. Goritsky, “Explicit construction of attracting integral manifolds for a dissipative hyperbolic equation”, J. Math. Sci. (N. Y.), 143:4 (2007), 3239–3252  mathnet  crossref  mathscinet  elib
    10. V. V. Chepyzhov, M. I. Vishik, “Non-autonomous 2D Navier–Stokes System with Singularly Oscillating External Force and its Global Attractor”, J Dyn Diff Equat, 19:3 (2007), 655  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    11. Chepyzhov, VV, “Averaging of nonautonomous damped wave equations with singularly oscillating external forces”, Journal de Mathematiques Pures et Appliquees, 90:5 (2008), 469  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    12. Vishik, MI, “Time Averaging of Global Attractors for Nonautonomous Wave Equations with Singularly Oscillating External Forces”, Doklady Mathematics, 78:2 (2008), 689  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    13. V V Chepyzhov, V Pata, M I Vishik, “Averaging of 2D Navier–Stokes equations with singularly oscillating forces”, Nonlinearity, 22:2 (2009), 351  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    14. Jean Louis Woukeng, David Dongo, “Multiscale homogenization of nonlinear hyperbolic equations with several time scales”, Acta Mathematica Scientia, 31:3 (2011), 843  crossref  mathscinet  zmath  isi  scopus
    15. Gabriel Nguetseng, Hubert Nnang, Nils Svanstedt, “Deterministic homogenization of quasilinear damped hyperbolic equations”, Acta Mathematica Scientia, 31:5 (2011), 1823  crossref  mathscinet  zmath  isi  scopus  scopus
    16. Hubert Nnang, “Deterministic homogenization of weakly damped nonlinear hyperbolic-parabolic equations”, Nonlinear Differ. Equ. Appl, 2011  crossref  mathscinet  isi  scopus  scopus
    17. Floden L., Persson J., “Homogenization of nonlinear dissipative hyperbolic problems exhibiting arbitrarily many spatial and temporal scales”, Netw. Heterog. Media, 11:4 (2016), 627–653  crossref  mathscinet  zmath  isi  scopus
    18. Bekmaganbetov K.A., Chechkin G.A., Chepyzhov V.V., Goritsky A.Yu., “Homogenization of trajectory attractors of 3D Navier–Stokes system with randomly oscillating force”, Discret. Contin. Dyn. Syst., 37:5 (2017), 2375–2393  crossref  mathscinet  zmath  isi  scopus
    19. Chechkin G.A., Chepyzhov V.V., Pankratov L.S., “Homogenization of Trajectory Attractors of Ginzburg-Landau Equations With Randomly Oscillating Terms”, Discrete Contin. Dyn. Syst.-Ser. B, 23:3 (2018), 1133–1154  crossref  mathscinet  isi  scopus  scopus
    20. Bekmaganbetov K.A., Chechkin G.A., Chepyzhov V.V., “Weak Convergence of Attractors of Reaction-Diffusion Systems With Randomly Oscillating Coefficients”, Appl. Anal., 98:1-2, SI (2019), 256–271  crossref  mathscinet  isi  scopus
    21. Cooper Sh., Savostianov A., “Homogenisation With Error Estimates of Attractors For Damped Semi-Linear Anisotropic Wave Equations”, Adv. Nonlinear Anal., 9:1 (2020), 745–787  crossref  isi
    22. Bekmaganbetov K.A., Chechkin G.A., Chepyzhov V.V., “Strong Convergence of Trajectory Attractors For Reaction-Diffusion Systems With Random Rapidly Oscillating Terms”, Commun. Pure Appl. Anal, 19:5 (2020), 2419–2443  crossref  isi
    23. Bekmaganbetov K.A., Chechkin G.A., Chepyzhov V.V., ““Strange Term” in Homogenization of Attractors of Reaction-Diffusion Equation in Perforated Domain”, Chaos Solitons Fractals, 140 (2020), 110208  crossref  mathscinet  isi
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