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

Dingshi Li; Xuemin Wang; Dingshi Li; Xuemin Wang

doi:10.3934/era.2020100

Electronic Research Archive

2021, Volume 29, Issue 2: 1969-1990. doi: 10.3934/era.2020100

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

Dingshi Li ^{1,2
,},
Xuemin Wang ^{1
,
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1.
School of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan 610031, China
2.
National Engineering Laboratory of, Integrated Transportation Big Data Application Technology, Chengdu, Sichuan 610031, China

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.
- Thin domain,
- regular random attractor,
- upper semicontinuity
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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Abstract

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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