Approximation of the random inertial manifold of singularly perturbed stochastic wave equations
Date
2014
Authors
Lv, Y.
Wang, W.
Roberts, A.
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Journal article
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Stochastics and Dynamics, 2014; 14(2):1350018-1-1350018-21
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Yan Lv, Wei Wang and A.J. Roberts
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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.
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© World Scientific Publishing Company