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- W3193430345 abstract "<p style='text-indent:20px;'>In this paper, we investigate a non-autonomous stochastic quasi-linear parabolic equation driven by multiplicative white noise by a Wong-Zakai approximation technique. The convergence of the solutions of quasi-linear parabolic equations driven by a family of processes with stationary increment to that of stochastic differential equation with white noise is obtained in the topology of <inline-formula><tex-math id=M2>$ L^2( {mathbb{R}}^N) $</tex-math></inline-formula> space. We establish the Wong-Zakai approximations of solutions in <inline-formula><tex-math id=M3>$ L^l( {mathbb{R}}^N) $</tex-math></inline-formula> for arbitrary <inline-formula><tex-math id=M4>$ lgeq q $</tex-math></inline-formula> in the sense of upper semi-continuity of their random attractors, where <inline-formula><tex-math id=M5>$ q $</tex-math></inline-formula> is the growth exponent of the nonlinearity. The <inline-formula><tex-math id=M6>$ L^l $</tex-math></inline-formula>-pre-compactness of attractors is proved by using the truncation estimate in <inline-formula><tex-math id=M7>$ L^q $</tex-math></inline-formula> and the higher-order bound of solutions.</p>" @default.
- W3193430345 created "2021-08-30" @default.
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- W3193430345 date "2021-01-01" @default.
- W3193430345 modified "2023-09-23" @default.
- W3193430345 title "Regularity of Wong-Zakai approximation for non-autonomous stochastic quasi-linear parabolic equation on <inline-formula><tex-math id=M1>$ {mathbb{R}}^N $</tex-math></inline-formula>" @default.
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- W3193430345 doi "https://doi.org/10.3934/era.2021056" @default.
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