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.
Citation:
T. V. Girya, I. D. Chueshov, “Inertial manifolds and stationary measures for stochastically perturbed dissipative dynamical systems”, Sb. Math., 186:1 (1995), 29–45
\Bibitem{GirChu95}
\by T.~V.~Girya, I.~D.~Chueshov
\paper Inertial manifolds and stationary measures for stochastically perturbed dissipative dynamical systems
\jour Sb. Math.
\yr 1995
\vol 186
\issue 1
\pages 29--45
\mathnet{http://mi.mathnet.ru/eng/sm2}
\crossref{https://doi.org/10.1070/SM1995v186n01ABEH000002}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1641664}
\zmath{https://zbmath.org/?q=an:0851.60036}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995RZ91900002}
Linking options:
https://www.mathnet.ru/eng/sm2
https://doi.org/10.1070/SM1995v186n01ABEH000002
https://www.mathnet.ru/eng/sm/v186/i1/p29
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