随机强迫Hamilton-Jacobi方程的均匀化

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-07-01 DOI:10.1016/j.anihpc.2020.11.001

Benjamin Seeger

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引用次数: 2

摘要

我们研究了一个Hamilton-Jacobi方程在空间彩色和时间白色的快速振荡噪声作用下的均匀化问题。结果表明，均匀化方程是确定的，并且，一般来说，噪声具有增强效应，对此我们提供了定量估计。作为应用，我们对带有小振幅噪声项的Hamilton-Jacobi方程进行了噪声敏感性分析，并确定了宏观增强效应的尺度。结果依赖于对大规模Hölder解的规律性的新的概率估计，这是独立的兴趣。

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Homogenization of a stochastically forced Hamilton-Jacobi equation

We study the homogenization of a Hamilton-Jacobi equation forced by rapidly oscillating noise that is colored in space and white in time. It is shown that the homogenized equation is deterministic, and, in general, the noise has an enhancement effect, for which we provide a quantitative estimate. As an application, we perform a noise sensitivity analysis for Hamilton-Jacobi equations forced by a noise term with small amplitude, and identify the scaling at which the macroscopic enhancement effect is felt. The results depend on new, probabilistic estimates for the large scale Hölder regularity of the solutions, which are of independent interest.

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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.