AMC-SS, Collaborative Research: Explorations in Stochastic Moving Boundary Value Problems

AMC-SS，协作研究：随机移动边值问题的探索

• 批准号: 0705260
• 负责人: Richard Sowers
• 金额: $ 18万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-08-01 至 2012-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0705260&HistoricalAwards=false
• 关键词: AMC; SS; Collaborative; Research; Explorations

This project outlines some problems which focus on the effect of noise on moving boundary problems. We are in particular interested in the mathematical foundations of a one-phase Stefan problem with additive noise. The noise can take on a number of forms, and the smoothness of the noise will affect the problems we can hope to consider. We pose a number of specific problems which, we hope, will resolve some fundamental issues in this area: existence, approximation, smoothness, and asymptotics.Moving boundary value problems are one of the key classes of partial differential equations. The simplest example is ice and water, where the motion of the boundary between the two depends on the local structure of the interface. Although these equations are difficult to study, there is a large body of literature on them. Since noise is ubiquitous in physical systems, it is natural to study the effect of noise on these systems. Although our research attempts to develop some of the foundations of stochastic moving boundary value problems, a number of applied areas (e.g. combustion and porous media) may benefit from the theory developed in this project.

本文概述了噪声对移动边界问题影响的一些问题。我们对具有加性噪声的单相Stefan问题的数学基础特别感兴趣。噪声可以采取多种形式，噪声的平滑程度将影响我们希望考虑的问题。我们提出了一些具体的问题，我们希望这些问题将解决这个领域的一些基本问题：存在性、逼近性、平滑性和渐近性。移动边值问题是一类重要的偏微分方程。最简单的例子是冰和水，两者之间边界的运动取决于界面的局部结构。虽然这些方程很难研究，但关于它们的文献很多。由于噪声在物理系统中无处不在，因此研究噪声对这些系统的影响是很自然的。虽然我们的研究试图发展随机移动边值问题的一些基础，但许多应用领域（例如燃烧和多孔介质）可能会从本项目中发展的理论中受益。