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Pullback measure attractors for non-autonomous stochastic lattice systems

Part of: Stochastic analysis Infinite-dimensional dissipative dynamical systems Equations and systems with randomness

Published online by Cambridge University Press:  22 November 2024

Shaoyue Mi ,
Dingshi Li  and
Tianhao Zeng
Shaoyue Mi
Affiliation:
School of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan 610031, P. R. China (mishaoyue@my.swjtu.edu.cn (S. Mi)) (corresponding authors)
Dingshi Li
Affiliation:
School of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan 610031, P. R. China
Tianhao Zeng
Affiliation:
School of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan 610031, P. R. China
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Abstract

The aim of this article is to study the asymptotic behaviour of non-autonomous stochastic lattice systems. We first show the existence and uniqueness of a pullback measure attractor. Moreover, when deterministic external forcing terms are periodic in time, we show the pullback measure attractors are periodic. We then study the upper semicontinuity of pullback measure attractors as the noise intensity goes to zero. Pullback asymptotic compact for a family of probability measures with respect to probability distributions of the solutions is demonstrated by using uniform a priori estimates for far-field values of solutions.

Keywords

dynamical behaviournon-autonoumouspullback measure attractorstochastic latticeasymptotic compact

MSC classification

Primary: 37L55: Infinite-dimensional random dynamical systems; stochastic equations
Secondary: 34F05: Equations and systems with randomness 37L30: Attractors and their dimensions, Lyapunov exponents 60H10: Stochastic ordinary differential equations

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 20
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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