Some dynamics behaviors for the nonautonomous stochastic fifth-order Swift–Hohenberg equation with additive white noise are considered. The existence of pullback random attractors for the nonautonomous stochastic fifth-order Swift–Hohenberg equation with some properties is mainly investigated on the bounded domain and unbounded domain, through the Ornstein–Uhlenbeck transformation and tail-term estimates. Furthermore, on the basis of some conditions, the finiteness of fractal dimension of random attractor is proved.

中文翻译：

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非自治随机五阶Swift–Hohenberg方程的分形维数

考虑了具有加性白噪声的非自治随机五阶Swift–Hohenberg方程的一些动力学行为。通过Ornstein-Uhlenbeck变换和尾项估计，主要研究有界和无界域上具有某些性质的非自治随机五阶Swift-Hohenberg方程的回撤随机吸引子的存在。此外，在一定条件下，证明了随机吸引子的分形维数是有限的。