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Volume 9, Number 4, 2019, Pages 1571-1588                                                                DOI:10.11948/2156-907X.20190021
The existence of random $\mathcal{D}$-pullback attractors for random dynamical system and its applications
Yongjun Li,Jinying Wei,Tinggang Zhao
Keywords:Random dynamical system, random pullback attractor, stochastic reaction diffusion equation.
      In this paper, we establish a result on the existence of random $\mathcal{D}$-pullback attractors for norm-to-weak continuous non-autonomous random dynamical system. Then we give a method to prove the existence of random $\mathcal{D}$-pullback attractors. As an application, we prove that the non-autonomous stochastic reaction diffusion equation possesses a random $\mathcal{D}$-pullback attractor in $H_0^1$ with polynomial growth of the nonlinear term.
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