Ergodicity and exponential mixing of the real Ginzburg-Landau equation with a degenerate noise

Xuhui Peng; Jianhua Huang; Rangrang Zhang

doi:10.1016/j.jde.2020.03.013

Ergodicity and exponential mixing of the real Ginzburg-Landau equation with a degenerate noise

Xuhui Peng
, Jianhua Huang
, Rangrang Zhang^*

^*此作品的通讯作者

数学学院

Hunan Normal University
National University of Defense Technology

科研成果: 期刊稿件 › 文章 › 同行评审

3 引用（Scopus）

摘要

In this paper, we establish the existence, uniqueness and attraction properties of an invariant measure for the real Ginzburg-Landau equation in the presence of a degenerate stochastic forcing acting only in four directions. The main challenge is to establish time asymptotic smoothing properties of the Markovian dynamics corresponding to this system. To achieve this, we propose a condition which only requires four noises.

源语言	英语
页（从-至）	3686-3720
页数	35
期刊	Journal of Differential Equations
卷	269
期	4
DOI	https://doi.org/10.1016/j.jde.2020.03.013
出版状态	已出版 - 5 8月 2020

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title = "Ergodicity and exponential mixing of the real Ginzburg-Landau equation with a degenerate noise",

abstract = "In this paper, we establish the existence, uniqueness and attraction properties of an invariant measure for the real Ginzburg-Landau equation in the presence of a degenerate stochastic forcing acting only in four directions. The main challenge is to establish time asymptotic smoothing properties of the Markovian dynamics corresponding to this system. To achieve this, we propose a condition which only requires four noises.",

keywords = "Ergodic, Exponential mixing, Malliavin calculus, Real Ginzburg-Landau equation",

author = "Xuhui Peng and Jianhua Huang and Rangrang Zhang",

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AU - Peng, Xuhui

AU - Huang, Jianhua

AU - Zhang, Rangrang

PY - 2020/8/5

Y1 - 2020/8/5

N2 - In this paper, we establish the existence, uniqueness and attraction properties of an invariant measure for the real Ginzburg-Landau equation in the presence of a degenerate stochastic forcing acting only in four directions. The main challenge is to establish time asymptotic smoothing properties of the Markovian dynamics corresponding to this system. To achieve this, we propose a condition which only requires four noises.

AB - In this paper, we establish the existence, uniqueness and attraction properties of an invariant measure for the real Ginzburg-Landau equation in the presence of a degenerate stochastic forcing acting only in four directions. The main challenge is to establish time asymptotic smoothing properties of the Markovian dynamics corresponding to this system. To achieve this, we propose a condition which only requires four noises.

KW - Ergodic

KW - Exponential mixing

KW - Malliavin calculus

KW - Real Ginzburg-Landau equation

UR - https://www.scopus.com/pages/publications/85081212673

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JO - Journal of Differential Equations

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ER -

Ergodicity and exponential mixing of the real Ginzburg-Landau equation with a degenerate noise

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