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The existence of random 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.
Abstract:
      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.