Approximation of the random inertial manifold of singularly perturbed stochastic wave equations

Yan Lv; Wei Wang; Anthony Roberts

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arXiv · 1209.0090

Approximation of the random inertial manifold of singularly perturbed stochastic wave equations

Yan Lv·Wei Wang·Anthony 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 interval.

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Yan Lv, Wei Wang, Anthony Roberts. 2012-09-01. Approximation of the random inertial manifold of singularly perturbed stochastic wave equations. https://arxiv.org/abs/1209.0090

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