Limiting behavior of dynamics for stochastic reaction-diffusion equations with additive noise on thin domains

Dingshi Li; Kening Lu; Bixiang Wang; Xiaohu Wang

doi:10.3934/dcds.2018009

Article Contents

2018, Volume 38, Issue 1: 187-208. Doi: 10.3934/dcds.2018009

This issue Previous Article Equidistribution with an error rate and Diophantine approximation over a local field of positive characteristic Next Article Single-point blow-up for a multi-component reaction-diffusion system

Limiting behavior of dynamics for stochastic reaction-diffusion equations with additive noise on thin domains

1.
School of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan 610031, China
2.
Department of Mathematics, Brigham Young University, Provo, Utah 84602, USA
3.
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China
4.
Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM 87801, USA

* Corresponding author: Xiaohu Wang, wangxiaohu@scu.edu.cn
* Corresponding author: Xiaohu Wang, wangxiaohu@scu.edu.cn

Received: January 31, 2017

Revised: July 31, 2017

Published: October 2017

This work was supported by NSFC (11271270, 11601446 and 11201320), NSF (1413603), Excellent Youth Scholars of Sichuan University (2016SCU04A15) and Fundamental Research Funds for the Central Universities (2682015CX059).

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Abstract

In this paper, we study the limiting behavior of dynamics for stochastic reaction-diffusion equations driven by an additive noise and a deterministic non-autonomous forcing on an (n+1)-dimensional thin region when it collapses into an n-dimensional region. We first established the existence of attractors and their properties for these equations on (n+1)-dimensional thin domains. We then show that these attractors converge to the random attractor of the limit equation under the usual semi-distance as the thinness goes to zero.

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Mathematics Subject Classification: Primary:35B40;Secondary:35B41, 37L30.

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