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 Uspekhi Mat. Nauk, 1998, Volume 53, Issue 4(322), Pages 77–124 (Mi umn57)

Theory of functionals that uniquely determine the asymptotic dynamics of infinite-dimensional dissipative systems

I. D. Chueshov

V. N. Karazin Kharkiv National University

DOI: https://doi.org/10.4213/rm57

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English version:
Russian Mathematical Surveys, 1998, 53:4, 731–776

Bibliographic databases:

UDC: 517.94
MSC: 37Lxx, 37K40, 35B40, 37B55

Citation: I. D. Chueshov, “Theory of functionals that uniquely determine the asymptotic dynamics of infinite-dimensional dissipative systems”, Uspekhi Mat. Nauk, 53:4(322) (1998), 77–124; Russian Math. Surveys, 53:4 (1998), 731–776

Citation in format AMSBIB
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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. I. D. Chueshov, “Analyticity of global attractors and determining nodes for a class of damped non-linear wave equations”, Sb. Math., 191:10 (2000), 1541–1559
2. A. V. Romanov, “Finite-dimensional dynamics on attractors of non-linear parabolic equations”, Izv. Math., 65:5 (2001), 977–1001
3. IGOR CHUESHOV, JINQIAO DUAN, BJÖRN SCHMALFUSS, “PROBABILISTIC DYNAMICS OF TWO-LAYER GEOPHYSICAL FLOWS”, Stoch. Dyn, 01:04 (2001), 451
4. JINQIAO DUAN, HONGJUNG GAO, BJÖRN SCHMALFUß, “STOCHASTIC DYNAMICS OF A COUPLED ATMOSPHERE–OCEAN MODEL”, Stoch. Dyn, 02:03 (2002), 357
5. Chueshov I., Duan Jinqiao, Schmalfuss B., “Determining functionals for random partial differential equations”, NoDEA Nonlinear Differential Equations Appl., 10:4 (2003), 431–454
6. Shcherbina A.S., “Gevrey regularity of the global attractor for the dissipative Zakharov system”, Dyn. Syst., 18:3 (2003), 201–225
7. Hale J.K., Raugel G., “Regularity, determining modes and Galerkin methods”, J. Math. Pures Appl. (9), 82:9 (2003), 1075–1136
8. Rekalo A.M., “Asymptotic behavior of solutions of nonlinear parabolic equations on two-layer thin domains”, Nonlinear Anal., 52:5 (2003), 1393–1410
9. Chueshov I., Lasiecka I., “Determining functionals for a class of second order in time evolution equations with applications to von Karman equations”, Analysis and Optimization of Differential Systems, International Federation for Information Processing, 121, 2003, 109–122
10. Chueshov, I, “Finite dimensionality of the attractor for a semilinear wave equation with nonlinear boundary dissipation”, Communications in Partial Differential Equations, 29:11–12 (2004), 1847
11. Gorban A.N., Karlin I.V., Zinovye A.Yu., “Constructive methods of invariant manifolds for kinetic problems”, Physics Reports-Review Section of Physics Letters, 396:4–6 (2004), 197–403
12. Ilyin, AA, “Sharp estimates for the number of degrees of freedom for the damped-driven 2-D Navier–Stokes equations”, Journal of Nonlinear Science, 16:3 (2006), 233
13. T. Yu. Semenova, “Approximation by step functions of functions belonging to Sobolev spaces and uniqueness of solutions of differential equations of the form $u-F(x,u,u')$”, Izv. Math., 71:1 (2007), 149–180
14. Okay Çelebi, Davut Uǧurlu, “Determining Functionals for the Strongly Damped Nonlinear Wave Equation”, Journal of Dynamical Systems and Geometric Theories, 5:2 (2007), 105
15. Chueshov I., Lasiecka I., Long-time behavior of second order evolution equations with nonlinear damping, Mem. Amer. Math. Soc., 195, no. 912, 2008, viii+183 pp.
16. Ilyin, AA, “The damped-driven 2D Navier–Stokes system on large elongated domains”, Journal of Mathematical Fluid Mechanics, 10:2 (2008), 159
17. T. Yu. Semenova, “Conditions on Determining Functionals for Subsets of Sobolev Space”, Math. Notes, 86:6 (2009), 831–841
18. Kalantarov V.K., Titi E.S., “Global attractors and determining modes for the 3D Navier–Stokes-Voight equations”, Chin. Ann. Math. Ser. B, 30:6 (2009), 697–714
19. Semenova T.Yu., “A class of determining functionals for quasilinear elliptic problems”, Moscow Univ. Math. Bull., 64:1 (2009), 11–15
20. Igor Chueshov, “Long-time dynamics of Kirchhoff wave models with strong nonlinear damping”, Journal of Differential Equations, 2011
21. Ermakov I.V., Kalinin Yu.N., Reitmann V., “Determining modes and almost periodic integrals for cocycles”, Differ Equ, 47:13 (2011), 1837–1852
22. Chueshov I., Kolbasin S., “Long-Time Dynamics in Plate Models With Strong Nonlinear Damping”, Commun Pure Appl Anal, 11:2 (2012), 659–674
23. Ciprian Foias, Michael S. Jolly, Rostyslav Kravchenko, Edriss S. Titi, “A determining form for the two-dimensional Navier–Stokes equations: The Fourier modes case”, J. Math. Phys, 53:11 (2012), 115623
24. I. V. Ermakov, V. Reitmann, “Determining functionals for the microwave heating system”, Vestnik St.Petersb. Univ.Math, 45:4 (2012), 153
25. Ülkü Dinlemez, “Global Existence, Uniqueness of Weak Solutions and Determining Functionals for Nonlinear Wave Equations”, APM, 03:05 (2013), 451
26. Soltanov K.N., Prykarpatski A.K., Blackmore D., “Long-Time Behavior of Solutions and Chaos in Reaction-Diffusion Equations”, Chaos Solitons Fractals, 99 (2017), 91–100
27. Cui H., Freitas M.M., Langa J.A., “Squeezing and Finite Dimensionality of Cocycle Attractors For 2D Stochastic Navier–Stokes Equation With Non-Autonomous Forcing”, Discrete Contin. Dyn. Syst.-Ser. B, 23:3 (2018), 1297–1324
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29. Bilgin B.A., Kalantarov V.K., “Existence of An Attractor and Determining Modes For Structurally Damped Nonlinear Wave Equations”, Physica D, 376:SI (2018), 15–22
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