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

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.

DOI: https://doi.org/10.4213/rm534

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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

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
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• https://doi.org/10.4213/rm534
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
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
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
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
5. M. I. Vishik, V. V. Chepyzhov, “Attractors of dissipative hyperbolic equations with singularly oscillating external forces”, Math. Notes, 79:4 (2006), 483–504
6. Zelik S., “Global averaging and parametric resonances in damped semilinear wave equations”, Proc. Roy. Soc. Edinburgh Sect. A, 136:5 (2006), 1053–1097
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
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
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
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
11. Chepyzhov, VV, “Averaging of nonautonomous damped wave equations with singularly oscillating external forces”, Journal de Mathematiques Pures et Appliquees, 90:5 (2008), 469
12. Vishik, MI, “Time Averaging of Global Attractors for Nonautonomous Wave Equations with Singularly Oscillating External Forces”, Doklady Mathematics, 78:2 (2008), 689
13. V V Chepyzhov, V Pata, M I Vishik, “Averaging of 2D Navier–Stokes equations with singularly oscillating forces”, Nonlinearity, 22:2 (2009), 351
14. Jean Louis Woukeng, David Dongo, “Multiscale homogenization of nonlinear hyperbolic equations with several time scales”, Acta Mathematica Scientia, 31:3 (2011), 843
15. Gabriel Nguetseng, Hubert Nnang, Nils Svanstedt, “Deterministic homogenization of quasilinear damped hyperbolic equations”, Acta Mathematica Scientia, 31:5 (2011), 1823
16. Hubert Nnang, “Deterministic homogenization of weakly damped nonlinear hyperbolic-parabolic equations”, Nonlinear Differ. Equ. Appl, 2011
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
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
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
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
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
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
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
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