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Limit measures and ergodicity of fractional stochastic reaction–diffusion equations on unbounded domains

Zhang Chen

School of Mathematics, Shandong University, Jinan, Shandong 250100, P. R. China

E-mail Address: zchen@sdu.edu.cn

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and

Bixiang Wang

https://orcid.org/0000-0001-5851-2453

Department of Mathematics, New Mexico Institute of Mixing and Technology, Socorro, NM 87801, USA

E-mail Address: bwang@nmt.edu

Corresponding author.

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https://doi.org/10.1142/S0219493721400128Cited by:17 (Source: Crossref)

This article is part of the issue:

Special Issue on Modern Topics on Stochastic Dynamics
Guest Editors: Jinqiao Duan & Alexandra Neamţu

Abstract

This paper deals with invariant measures of fractional stochastic reaction–diffusion equations on unbounded domains with locally Lipschitz continuous drift and diffusion terms. We first prove the existence and regularity of invariant measures, and then show the tightness of the set of all invariant measures of the equation when the noise intensity varies in a bounded interval. We also prove that every limit of invariant measures of the perturbed systems is an invariant measure of the corresponding limiting system. Under further conditions, we establish the ergodicity and the exponentially mixing property of invariant measures.

Keywords:

AMSC: 37L40, 37L55, 60H15

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