Rn 上分数随机延迟金兹堡-朗道方程的不变量研究。

IF 2.6 4区工程技术 Q1 Mathematics

Mathematical Biosciences and Engineering Pub Date : 2024-03-15 DOI:10.3934/mbe.2024241

Hong Lu, Linlin Wang, Mingji Zhang

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引用次数: 0

摘要

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。

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

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.

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来源期刊

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).