Averaging principle for one dimensional stochastic Burgers equation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:265

Article

Dong, Zhao^1,2  Sun, Xiaobin³  Xiao, Hui^1,2,4  Zhai, Jianliang⁵ 

[1] Chinese Acad Sci, Acad Math & Syst Sci, RCSDS, Beijing 100190, Peoples R China

[2] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100190, Peoples R China

[3] Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Jiangsu, Peoples R China

[4] Univ Bretagne Sud, LMBA UMR CNRS 6205, Vannes, France

[5] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China

关键词: Stochastic Burgers' equation;    Averaging principle;    Ergodicity;    Invariant measure;    Strong convergence;    Weak convergence;   

DOI  :  10.1016/j.jde.2018.06.020

来源: Elsevier

【 摘 要 】

In this paper, we consider the averaging principle for one dimensional stochastic Burgers equation with slow and fast time-scales. Under some suitable conditions, we show that the slow component strongly converges to the solution of the corresponding averaged equation. Meanwhile, when there is no noise in the slow component equation, we also prove that the slow component weakly converges to the solution of the corresponding averaged equation with the order of convergence 1 - r, for any 0 < r < 1. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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