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

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The first author is supported by CTBU Grant (KFJJ2018101, ZDPTTD201909), Chongqing NSF Grant cstc2019jcyj-msxmX0115 and China NSF Grant 11871122

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  • 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 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.

    Mathematics Subject Classification: Primary:35R60, 35B40, 35B41, 35B65;Secondary:60H15.


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