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|Title:||Approximation of the random inertial manifold of singularly perturbed stochastic wave equations|
|Citation:||Stochastics and Dynamics, 2014; 14(2):1350018-1-1350018-21|
|Publisher:||World Scientific Publishing|
|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|
|Appears in Collections:||Mathematical Sciences publications|
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