Wong-Zakai approximations and attractors for stochastic wave equations driven by additive noise
The authors investigate the asymptotic behavior of the solutions of the stochastic wave equation driven by an additive white noise on unbounded domains and its Wong-Zakai approximation. The main idea of Wong-Zakai approximation is to use deterministic differential equations to approximate the solutions of the stochastic differential equations. In the article, Brownian motion is approximated using the Euler approximation. The authors prove the existence and uniqueness of tempered pullback attractors for stochastic wave equation and its Wong-Zakai approximation. Then, they 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.
scientific article; zbMATH DE number 7360488
scientific article