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This article is cited in 28 scientific papers (total in 28 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.
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
Linking options:
https://www.mathnet.ru/eng/sm2https://doi.org/10.1070/SM1995v186n01ABEH000002 https://www.mathnet.ru/eng/sm/v186/i1/p29
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Abstract page: | 516 | Russian version PDF: | 137 | English version PDF: | 10 | References: | 55 | First page: | 1 |
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