### Electronic Research Archive

2021, Issue 2: 1969-1990. doi: 10.3934/era.2020100
Special Issues

# Regular random attractors for non-autonomous stochastic reaction-diffusion equations on thin domains

• Received: 01 February 2020 Revised: 01 July 2020 Published: 23 September 2020
• Primary: 60H15, 35B40, 58F11, 58F36

• This paper deals with the limiting dynamical behavior of non-autonomous stochastic reaction-diffusion equations on thin domains. Firstly, we prove the existence and uniqueness of the regular random attractor. Then we prove the upper semicontinuity of the regular random attractors for the equations on a family of $(n+1)$-dimensional thin domains collapses onto an $n$-dimensional domain.

Citation: Dingshi Li, Xuemin Wang. Regular random attractors for non-autonomous stochastic reaction-diffusion equations on thin domains[J]. Electronic Research Archive, 2021, 29(2): 1969-1990. doi: 10.3934/era.2020100

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• This paper deals with the limiting dynamical behavior of non-autonomous stochastic reaction-diffusion equations on thin domains. Firstly, we prove the existence and uniqueness of the regular random attractor. Then we prove the upper semicontinuity of the regular random attractors for the equations on a family of $(n+1)$-dimensional thin domains collapses onto an $n$-dimensional domain.

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