Wong-Zakai Approximations and Long Term Behavior of Stochastic Partial Differential Equations

作者：Lu, Kening^*; Wang, Bixiang

来源：Journal of Dynamics and Differential Equations, 2019, 31(3): 1341-1371.

DOI：10.1007/s10884-017-9626-y

• Random attractor
• Upper semicontinuity
• White noise
• Wong-Zakai approximation
• Stochastic equation

In this paper we study the Wong-Zakai approximations given by a stationary process via the Wiener shift and their associated long term pathwise behavior for the stochastic partial differential equations driven by a white noise. We prove that the approximate equation has a pullback random attractor under much weaker conditions than the original stochastic equation. When the stochastic partial differential equation is driven by a linear multiplicative noise or additive white noise, we prove the convergence of solutions of Wong-Zakai approximations and the upper semicontinuity of random attractors of the approximate random system as the size of approximation approaches zero.

• 出版日期2019-9