Dynamics and Wong-Zakai Approximations of Stochastic Nonlocal PDEs with Long Time Memory

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-02 DOI:10.1007/s12346-024-01080-2

Jiaohui Xu, Tomás Caraballo, José Valero

引用次数: 0

Abstract

In this paper, a combination of Galerkin’s method and Dafermos’ transformation is first used to prove the existence and uniqueness of solutions for a class of stochastic nonlocal PDEs with long time memory driven by additive noise. Next, the existence of tempered random attractors for such equations is established in an appropriate space for the analysis of problems with delay and memory. Eventually, the convergence of solutions of Wong-Zakai approximations and upper semicontinuity of random attractors of the approximate random system, as the step sizes of approximations approach zero, are analyzed in a detailed way.

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具有长时记忆的随机非局部 PDE 的动力学与 Wong-Zakai 近似值

本文首先结合 Galerkin 方法和 Dafermos 变换，证明了一类由加性噪声驱动的具有长时记忆的随机非局部 PDEs 的解的存在性和唯一性。接着，在分析具有延迟和记忆的问题的适当空间中，建立了这类方程的有节制随机吸引子的存在性。最后，详细分析了当近似步长趋近于零时，Wong-Zakai 近似解的收敛性和近似随机系统随机吸引子的上半连续性。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.