Mathematical Sciences: Parabolic Partial Differential Equations in Nonsmooth Domains.

数学科学：非光滑域中的抛物型偏微分方程。

• 批准号: 9103046
• 负责人: Russell Brown
• 金额: $ 4.13万
• 依托单位: University of Kentucky Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-15 至 1994-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9103046&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Parabolic; Partial; Differential

This project will study parabolic partial differential equations in domains with rough boundaries. Using as a frame of reference recent results on the heat equation, efforts will be made to establish regularity properties of solutions to higher order parabolic equations and noncylindrical domains. Main issues to be dealt with are the spectral properties of the domains and properties of the trace semigroup. In addition to solving basic questions in differential equations, the result of this project have implications to applied areas such as probability, physics and engineering. In particular problems in colloids and furtive materials might benefit from this investment.

本课题将研究具有粗糙边界的区域中的抛物型偏微分方程解。以热方程的最新结果为参照，建立高阶抛物型方程和非圆柱型区域解的正则性。要处理的主要问题是定义域的谱性质和迹半群的性质。除了解决微分方程中的基本问题外，这个项目的结果还对概率、物理和工程等应用领域有影响。特别是，胶体和隐秘材料方面的问题可能会从这项投资中受益。