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Pullback attractor in $H^{1}$ for nonautonomous stochastic reaction-diffusion equations on $\mathbb{R}^n$

  • * Corresponding author: Yuncheng You

    * Corresponding author: Yuncheng You
The second author is supported by NSF grant of China (Nos. 11671142 and 11371087), Science and Technology Commission of Shanghai Municipality (STCSM) (grant No. 13dz2260400) and Shanghai Leading Academic Discipline Project (No. B407).
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  • In this paper we study the asymptotic dynamics of the weak solutions of nonautonomous stochastic reaction-diffusion equations driven by a time-dependent forcing term and the multiplicative noise. By conducting the uniform estimates we show that the cocycle generated by this SRDE has a pullback $(L^2, H^1)$ absorbing set and it is pullback asymptotically compact through the pullback flattening approach. The existence of a pullback $(L^2, H^1)$ random attractor for this random dynamical system in space $H^{1}(\mathbb{R}^{n})$ is proved.

    Mathematics Subject Classification: 35B40, 35B41, 35R60, 37L30.


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