Studies on invariant measures of fractional stochastic delay Ginzburg-Landau equations on Rn.

IF 2.6 4区 工程技术 Q1 Mathematics
Hong Lu, Linlin Wang, Mingji Zhang
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引用次数: 0

Abstract

This paper is concerned with invariant measures of fractional stochastic delay Ginzburg-Landau equations on the entire space $ \mathbb{R}^n $. We first derive the uniform estimates and the mean-square uniform smallness of the tails of solutions in corresponding space. Then we deduce the weak compactness of a set of probability distributions of the solutions applying the Ascoli-Arzel$ \grave{a} $. We finally prove the existence of invariant measures by applying Krylov-Bogolyubov's method.

Rn 上分数随机延迟金兹堡-朗道方程的不变量研究。
本文关注整个空间 $\mathbb{R}^n $ 上分数随机延迟金兹堡-朗道方程的不变度量。我们首先推导了相应空间中解的均匀估计和均方均匀小尾。然后,我们应用阿斯科利-阿尔泽尔(Ascoli-Arzel)$ \grave{a} $ 推导出一组解的概率分布的弱紧凑性。最后,我们运用克雷洛夫-波格廖布夫方法证明了不变度量的存在。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Mathematical Biosciences and Engineering
Mathematical Biosciences and Engineering 工程技术-数学跨学科应用
CiteScore
3.90
自引率
7.70%
发文量
586
审稿时长
>12 weeks
期刊介绍: Mathematical Biosciences and Engineering (MBE) is an interdisciplinary Open Access journal promoting cutting-edge research, technology transfer and knowledge translation about complex data and information processing. MBE publishes Research articles (long and original research); Communications (short and novel research); Expository papers; Technology Transfer and Knowledge Translation reports (description of new technologies and products); Announcements and Industrial Progress and News (announcements and even advertisement, including major conferences).
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