Dynamics of non-autonomous stochastic rotational inertia and Kelvin–Voigt dissipative plate equations with Laplace-multiplier noise

In this paper, we investigate the asymptotic dynamics of a non-autonomous stochastic rotational inertia and Kelvin–Voigt dissipative plate equation with multiplicative noise. The noise is multiplied by a Laplace operator which is unbounded. We establish the existence and upper semi-continuity of pullback attractors in H2(O)×H01(O)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^2({\mathcal {O}}) \times H^1_0({\mathcal {O}})$$\end{document}, and, in particular, the upper semi-continuity is proved to be uniform for sections located in finite time. To overcome the technical difficulty arising from the low regularity of solutions and from the high-order term Δ2u\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta ^2 u$$\end{document} involved in the equation, a decomposition technique of the solution operator is employed to derive the crucial pullback limit-set compactness of the system. The theoretical result of this paper can be regarded as a complement of the previous work (Yin and Xu in Math Methods Appl Sci 43:4486–4517, 2020) on the upper semi-continuity of pullback attractors, where a uniformity in time parameter (rather than in sections of the attractor) was studied.