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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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Sbornik: Mathematics, 1995, 186:1, 29–45
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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
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\jour Mat. Sb.
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\yr 1995
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This publication is cited in the following articles:
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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
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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
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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
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Jinqiao Duan, Kening Lu, Björn Schmalfuss, “Smooth Stable and Unstable Manifolds for Stochastic Evolutionary Equations”, J Dyn Diff Equat, 16:4 (2004), 949
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Chueshov, ID, “Averaging of attractors and inertial manifolds for parabolic PDE with random coefficients”, Advanced Nonlinear Studies, 5:4 (2005), 461
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Kening Lu, Björn Schmalfuß, “Invariant manifolds for stochastic wave equations”, Journal of Differential Equations, 236:2 (2007), 460
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Björn Schmalfuss, Klaus R. Schneider, “Invariant Manifolds for Random Dynamical Systems with Slow and Fast Variables”, J Dyn Diff Equat, 20:1 (2008), 133
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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
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Igor Chueshov, Björn Schmalfuß, “Master-slave synchronization and invariant manifolds for coupled stochastic systems”, J. Math. Phys, 51:10 (2010), 102702
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Armen Shirikyan, Sergey Zelik, “Exponential attractors for random dynamical systems and applications”, Stoch PDE: Anal Comp, 2013
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Wang W., Roberts A.J., “Macroscopic Reduction for Stochastic Reaction-Diffusion Equations”, IMA J. Appl. Math., 78:6 (2013), 1237–1264
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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
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Davit Martirosyan, “Exponential mixing for the white-forced damped nonlinear wave equation”, EECT, 3:4 (2014), 645
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