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Wong-Zakai approximations and attractors for stochastic wave equations driven by additive noise

This work was supported by NSFC (11831012, 11971394 and 11871049), Fundamental Research Funds for the Central Universities (YJ201646, 2682019LK02), Sichuan Science and Technology Program (2019YJ0215) and International Visiting Program for Excellent Young Scholars of SCU
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  • In this paper, we study the Wong-Zakai approximations given by a stationary process via Euler approximation of Brownian motion and the associated long term behavior of the stochastic wave equation driven by an additive white noise on unbounded domains. We first prove the existence and uniqueness of tempered pullback attractors for stochastic wave equation and its Wong-Zakai approximation. Then, we show that the attractor of the Wong-Zakai approximate equation converges to the one of the stochastic wave equation driven by additive noise as the correlation time of noise approaches zero.

    Mathematics Subject Classification: Primary: 60H15; 35B40; 35B41.


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