随机强迫Hamilton-Jacobi方程的均匀化

IF 1.8 1区数学 Q1 MATHEMATICS, APPLIED

Annales De L Institut Henri Poincare-Analyse Non Lineaire 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

Annales De L Institut Henri Poincare-Analyse Non Lineaire 数学-应用数学

CiteScore

4.10

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Nonlinear Analysis section of the Annales de l''Institut Henri Poincaré is an international journal created in 1983 which publishes original and high quality research articles. It concentrates on all domains concerned with nonlinear analysis, specially applicable to PDE, mechanics, physics, economy, without overlooking the numerical aspects.