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The Wong-Zakai approximations of stochastic inertial manifolds for evolution equations
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Abstract
In this paper, we study the Wong-Zakai approximations given by a stationary process via the Wiener shift and their associated dynamics of a class of stochastic evolution equations with an additive white noise. We show the existence of solutions as well as stochastic inertial manifolds for both the approximation systems and the original system. Furthermore, we prove that solutions and stochastic inertial manifolds of the approximation system are approaching to those of the original system respectively in the sense of probability.
Title: The Wong-Zakai approximations of stochastic inertial manifolds for evolution equations
Description:
Abstract
In this paper, we study the Wong-Zakai approximations given by a stationary process via the Wiener shift and their associated dynamics of a class of stochastic evolution equations with an additive white noise.
We show the existence of solutions as well as stochastic inertial manifolds for both the approximation systems and the original system.
Furthermore, we prove that solutions and stochastic inertial manifolds of the approximation system are approaching to those of the original system respectively in the sense of probability.
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