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https://hdl.handle.net/2440/100643
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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 1793-6799 |
Statement of Responsibility: | 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 |
DOI: | 10.1142/S0219493713500184 |
Grant ID: | http://purl.org/au-research/grants/arc/DP0774311 http://purl.org/au-research/grants/arc/DP0988738 |
Published version: | http://dx.doi.org/10.1142/s0219493713500184 |
Appears in Collections: | Aurora harvest 7 Mathematical Sciences publications |
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