High-order Wong-Zakai approximations for non-autonomous stochastic \begin{document}$ p $\end{document}-Laplacian equations on \begin{document}$ \mathbb{R}^N $\end{document}

Wenqiang Zhao, Chongqing Key Laboratory of Social Economy and Applied Statistics, School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China, Yijin Zhang, Chongqing Key Laboratory of Social Economy and Applied Statistics, School of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
2020 Communications on Pure and Applied Analysis  
In this paper, we investigate the approximations of stochastic p-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 p-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
more » ... 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 q-times integrable functions, where the upper semi-continuity of the attractors of the approximation equations is well established.
doi:10.3934/cpaa.2020265 fatcat:nf6b5vhgzvgtppfldsjkouqzwy