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

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

Full text: PDF file (523 kB)
References: PDF file   HTML file

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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    Citing articles on Google Scholar: Russian citations, English citations
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    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  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. A. V. Romanov, “Finite-dimensional dynamics on attractors of non-linear parabolic equations”, Izv. Math., 65:5 (2001), 977–1001  mathnet  crossref  crossref  mathscinet  zmath
    3. IGOR CHUESHOV, JINQIAO DUAN, BJÖRN SCHMALFUSS, “PROBABILISTIC DYNAMICS OF TWO-LAYER GEOPHYSICAL FLOWS”, Stoch. Dyn, 01:04 (2001), 451  crossref  mathscinet
    4. JINQIAO DUAN, HONGJUNG GAO, BJÖRN SCHMALFUß, “STOCHASTIC DYNAMICS OF A COUPLED ATMOSPHERE–OCEAN MODEL”, Stoch. Dyn, 02:03 (2002), 357  crossref  mathscinet
    5. Chueshov I., Duan Jinqiao, Schmalfuss B., “Determining functionals for random partial differential equations”, NoDEA Nonlinear Differential Equations Appl., 10:4 (2003), 431–454  crossref  mathscinet  zmath  isi  scopus  scopus
    6. Shcherbina A.S., “Gevrey regularity of the global attractor for the dissipative Zakharov system”, Dyn. Syst., 18:3 (2003), 201–225  crossref  mathscinet  zmath  isi  scopus  scopus
    7. Hale J.K., Raugel G., “Regularity, determining modes and Galerkin methods”, J. Math. Pures Appl. (9), 82:9 (2003), 1075–1136  crossref  mathscinet  zmath  isi  scopus
    8. Rekalo A.M., “Asymptotic behavior of solutions of nonlinear parabolic equations on two-layer thin domains”, Nonlinear Anal., 52:5 (2003), 1393–1410  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    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  mathscinet  isi
    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  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    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  crossref  mathscinet  isi  elib  scopus  scopus
    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  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    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  crossref  mathscinet  zmath
    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.  mathscinet  zmath  isi
    16. Ilyin, AA, “The damped-driven 2D Navier–Stokes system on large elongated domains”, Journal of Mathematical Fluid Mechanics, 10:2 (2008), 159  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    17. T. Yu. Semenova, “Conditions on Determining Functionals for Subsets of Sobolev Space”, Math. Notes, 86:6 (2009), 831–841  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    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  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    19. Semenova T.Yu., “A class of determining functionals for quasilinear elliptic problems”, Moscow Univ. Math. Bull., 64:1 (2009), 11–15  crossref  mathscinet  zmath  elib  elib  scopus
    20. Igor Chueshov, “Long-time dynamics of Kirchhoff wave models with strong nonlinear damping”, Journal of Differential Equations, 2011  crossref  mathscinet  isi  scopus  scopus
    21. Ermakov I.V., Kalinin Yu.N., Reitmann V., “Determining modes and almost periodic integrals for cocycles”, Differ Equ, 47:13 (2011), 1837–1852  crossref  mathscinet  zmath  isi  elib  scopus
    22. Chueshov I., Kolbasin S., “Long-Time Dynamics in Plate Models With Strong Nonlinear Damping”, Commun Pure Appl Anal, 11:2 (2012), 659–674  crossref  mathscinet  zmath  isi  scopus  scopus
    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  crossref  mathscinet  zmath  isi  scopus  scopus
    24. I. V. Ermakov, V. Reitmann, “Determining functionals for the microwave heating system”, Vestnik St.Petersb. Univ.Math, 45:4 (2012), 153  crossref  mathscinet  mathscinet  zmath  elib  elib  scopus
    25. Ülkü Dinlemez, “Global Existence, Uniqueness of Weak Solutions and Determining Functionals for Nonlinear Wave Equations”, APM, 03:05 (2013), 451  crossref
    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  crossref  mathscinet  zmath  isi  scopus  scopus
    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  crossref  mathscinet  isi  scopus  scopus
    28. 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  crossref  mathscinet  isi  scopus  scopus
    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  crossref  mathscinet  isi  scopus
    30. Bilgin B., Kalantarov V., “Determining Functionals For Damped Nonlinear Wave Equations”, Complex Var. Elliptic Equ., 63:7-8, SI (2018), 931–944  crossref  mathscinet  zmath  isi  scopus
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