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Random dynamics of fractional nonclassical diffusion equations driven by colored noise

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  • The random dynamics in $ H^s(\mathbb{R}^n) $ with $ s\in (0,1) $ is investigated for the fractional nonclassical diffusion equations driven by colored noise. Both existence and uniqueness of pullback random attractors are established for the equations with a wide class of nonlinear diffusion terms. In the case of additive noise, the upper semi-continuity of these attractors is proved as the correlation time of the colored noise approaches zero. The methods of uniform tail-estimate and spectral decomposition are employed to obtain the pullback asymptotic compactness of the solutions in order to overcome the non-compactness of the Sobolev embedding on an unbounded domain.

    Mathematics Subject Classification: Primary: 37L55; Secondary: 35B40, 60H15.


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