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Mat. Sb., 1995, Volume 186, Number 1, Pages 29–46 (Mi msb2)  

This article is cited in 13 scientific papers (total in 13 papers)

Inertial manifolds and stationary measures for stochastically perturbed dissipative dynamical systems

T. V. Girya, I. D. Chueshov

Kharkiv State University

Abstract: We prove the existence of inertial manifolds for a semilinear dynamical system perturbed by additive ‘white noise’. This manifold is generated by a certain predictable stationary vector process $\Phi_t(\omega)$. We study properties of this process as well as the properties of the induced finite-dimensional stochastic system on the manifold (inertial form). The results obtained allow us to prove for the original stochastic system a theorem on stabilization of stationary solutions to a unique invariant measure. This measure is uniquely defined by the probability distribution of the process $\Phi_t(\omega)$ and the form of the invariant measure corresponding to the inertial form.

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English version:
Sbornik: Mathematics, 1995, 186:1, 29–45

Bibliographic databases:

UDC: 517.919
MSC: 60G10, 34D45
Received: 24.02.1994

Citation: T. V. Girya, I. D. Chueshov, “Inertial manifolds and stationary measures for stochastically perturbed dissipative dynamical systems”, Mat. Sb., 186:1 (1995), 29–46; Sb. Math., 186:1 (1995), 29–45

Citation in format AMSBIB
\by T.~V.~Girya, I.~D.~Chueshov
\paper Inertial manifolds and stationary measures for stochastically perturbed dissipative dynamical systems
\jour Mat. Sb.
\yr 1995
\vol 186
\issue 1
\pages 29--46
\jour Sb. Math.
\yr 1995
\vol 186
\issue 1
\pages 29--45

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    This publication is cited in the following articles:
    1. I. D. Chueshov, “Approximate inertial manifolds of exponential order for semilinear parabolic equations subjected to additive white noise”, J Dyn Diff Equat, 7:4 (1995), 549  crossref  mathscinet  zmath
    2. Igor D. Chueshov, Pierre A. Vuillermot, “Long-time behavior of solutions to a class of stochastic parabolic equations with homogeneous white noise: itô's case”, Stochastic Analysis and Applications, 18:4 (2000), 581  crossref  mathscinet  zmath
    3. S.I. Dudov, I.V. Zlatorunskaya, “Uniform estimate of a compact convex set by a ball in an arbitrary norm”, Sb. Math, 191:10 (2000), 1433  mathnet  crossref  mathscinet  zmath
    4. Jinqiao Duan, Kening Lu, Björn Schmalfuss, “Smooth Stable and Unstable Manifolds for Stochastic Evolutionary Equations”, J Dyn Diff Equat, 16:4 (2004), 949  crossref  mathscinet  zmath
    5. Chueshov, ID, “Averaging of attractors and inertial manifolds for parabolic PDE with random coefficients”, Advanced Nonlinear Studies, 5:4 (2005), 461  crossref  mathscinet  zmath  isi
    6. Kening Lu, Björn Schmalfuß, “Invariant manifolds for stochastic wave equations”, Journal of Differential Equations, 236:2 (2007), 460  crossref  mathscinet  zmath
    7. Björn Schmalfuss, Klaus R. Schneider, “Invariant Manifolds for Random Dynamical Systems with Slow and Fast Variables”, J Dyn Diff Equat, 20:1 (2008), 133  crossref  mathscinet  zmath  isi
    8. María J. Garrido-Atienza, Kening Lu, Björn Schmalfuß, “Unstable invariant manifolds for stochastic PDEs driven by a fractional Brownian motion”, Journal of Differential Equations, 248:7 (2010), 1637  crossref  mathscinet  zmath
    9. Igor Chueshov, Björn Schmalfuß, “Master-slave synchronization and invariant manifolds for coupled stochastic systems”, J. Math. Phys, 51:10 (2010), 102702  crossref  mathscinet  zmath
    10. Armen Shirikyan, Sergey Zelik, “Exponential attractors for random dynamical systems and applications”, Stoch PDE: Anal Comp, 2013  crossref  mathscinet
    11. Wang W., Roberts A.J., “Macroscopic Reduction for Stochastic Reaction-Diffusion Equations”, IMA J. Appl. Math., 78:6 (2013), 1237–1264  crossref  mathscinet  zmath  isi
    12. Li J., Lu K., Bates P., “Normally Hyperbolic Invariant Manifolds for Random Dynamical Systems: Part I - Persistence”, Trans. Am. Math. Soc., 365:11 (2013), 5933–5966  crossref  mathscinet  zmath  isi
    13. Davit Martirosyan, “Exponential mixing for the white-forced damped nonlinear wave equation”, EECT, 3:4 (2014), 645  crossref  mathscinet  zmath
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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