High-order Wong-Zakai approximations for non-autonomous stochastic $ p $ -Laplacian equations on $ \mathbb{R}^N $
Wenqiang Zhao, Yijin Zhang · Communications on Pure & Applied Analysis · 2020
In this paper, we investigate the approximations of stochastic \begin{document}$ p $\end{document} -Laplacian equation with additive white noise by a family of piecewise deterministic partial differential equations driven by a stationary stochastic process. We firstly obtain the tempered pullback attractors for the random \begin{document}$ p $\end{document} -Laplacian equation with a general diffusion. We secondly prove the convergence of solutions and the upper semi-continuity of pullback attractors of the Wong-Zakai approximation equations in a Hilbert space for the additive case. Thirdly, by a truncation technique, the uniform compactness of pullback attractor with respect to the quantity of approximations is derived in the space of \begin{document}$ q $\end{document} -times integrable functions, where the upper semi-continuity of the attractors of the approximation equations is well established.