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This article is cited in 30 scientific papers (total in 30 papers)
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
Received: 15.09.1997
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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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
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A. V. Romanov, “Finite-dimensional dynamics on attractors of non-linear parabolic equations”, Izv. Math., 65:5 (2001), 977–1001
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IGOR CHUESHOV, JINQIAO DUAN, BJÖRN SCHMALFUSS, “PROBABILISTIC DYNAMICS OF TWO-LAYER GEOPHYSICAL FLOWS”, Stoch. Dyn, 01:04 (2001), 451
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JINQIAO DUAN, HONGJUNG GAO, BJÖRN SCHMALFUß, “STOCHASTIC DYNAMICS OF A COUPLED ATMOSPHERE–OCEAN MODEL”, Stoch. Dyn, 02:03 (2002), 357
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Chueshov I., Duan Jinqiao, Schmalfuss B., “Determining functionals for random partial differential equations”, NoDEA Nonlinear Differential Equations Appl., 10:4 (2003), 431–454
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Shcherbina A.S., “Gevrey regularity of the global attractor for the dissipative Zakharov system”, Dyn. Syst., 18:3 (2003), 201–225
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Hale J.K., Raugel G., “Regularity, determining modes and Galerkin methods”, J. Math. Pures Appl. (9), 82:9 (2003), 1075–1136
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Rekalo A.M., “Asymptotic behavior of solutions of nonlinear parabolic equations on two-layer thin domains”, Nonlinear Anal., 52:5 (2003), 1393–1410
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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
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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
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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
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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
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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
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Okay Çelebi, Davut Uǧurlu, “Determining Functionals for the Strongly Damped Nonlinear Wave Equation”, Journal of Dynamical Systems and Geometric Theories, 5:2 (2007), 105
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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.
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Ilyin, AA, “The damped-driven 2D Navier–Stokes system on large elongated domains”, Journal of Mathematical Fluid Mechanics, 10:2 (2008), 159
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T. Yu. Semenova, “Conditions on Determining Functionals for Subsets of Sobolev Space”, Math. Notes, 86:6 (2009), 831–841
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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
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Semenova T.Yu., “A class of determining functionals for quasilinear elliptic problems”, Moscow Univ. Math. Bull., 64:1 (2009), 11–15
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Igor Chueshov, “Long-time dynamics of Kirchhoff wave models with strong nonlinear damping”, Journal of Differential Equations, 2011
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Ermakov I.V., Kalinin Yu.N., Reitmann V., “Determining modes and almost periodic integrals for cocycles”, Differ Equ, 47:13 (2011), 1837–1852
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Chueshov I., Kolbasin S., “Long-Time Dynamics in Plate Models With Strong Nonlinear Damping”, Commun Pure Appl Anal, 11:2 (2012), 659–674
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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
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I. V. Ermakov, V. Reitmann, “Determining functionals for the microwave heating system”, Vestnik St.Petersb. Univ.Math, 45:4 (2012), 153
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Ülkü Dinlemez, “Global Existence, Uniqueness of Weak Solutions and Determining Functionals for Nonlinear Wave Equations”, APM, 03:05 (2013), 451
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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
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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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Kalantarov V.K., Titi E.S., “Global Stabilization of the Navier–Stokes-Voight and the Damped Nonlinear Wave Equations By Finite Number of Feedback Controllers”, Discrete Contin. Dyn. Syst.-Ser. B, 23:3 (2018), 1325–1345
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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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