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Type: Journal article
Title: Approximation of the random inertial manifold of singularly perturbed stochastic wave equations
Author: Lv, Y.
Wang, W.
Roberts, A.
Citation: Stochastics and Dynamics, 2014; 14(2):1350018-1-1350018-21
Publisher: World Scientific Publishing
Issue Date: 2014
ISSN: 0219-4937
Statement of
Yan Lv, Wei Wang and A.J. Roberts
Abstract: By applying Rohlin’s result on the classification of homomorphisms of Lebesgue space, the random inertial manifold of a stochastic damped nonlinear wave equations with singular perturbation is proved to be approximated almost surely by that of a stochastic nonlinear heat equation which is driven by a new Wiener process depending on the singular perturbation parameter. This approximation can be seen as the Smolukowski-Kramers approximation as time goes to infinity. However, as time goes infinity, the approximation changes with the small parameter, which is different from the approximation on a finite time interval.
Keywords: Random inertial manifold; singularly perturbed stochastic wave equation; Lebesgue space; homomorphism
Rights: © World Scientific Publishing Company
RMID: 0030008019
DOI: 10.1142/S0219493713500184
Grant ID:
Appears in Collections:Mathematical Sciences publications

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