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Random pullback attractor for a non-autonomous modified Swift-Hohenberg equation with multiplicative noise
Yongjun Li,Jinying Wei,Zhengzhi Lu
Keywords:Swift-Hohenberg equation, $\mathcal{D}$-pullback attractor, Non-autonomous random dynamical system
Abstract:
      In this paper, we study long time behavior of a non-autonomous stochastic modified Swift-Hohenberg equation with multiplicative noise in stratonovich sense. We shown that a random $\mathcal{D}$-pullback attractor exists in $H_0^2$ for the corresponding non-autonomous random dynamical system. Due to the stochastic term, the estimate are delicate, the Ornstein-Uhlenbeck(O-U) transformation and its properties are used to over the difficulty that the stochastic term bring to us.