Mathematical Sciences: Homogenization and Oscillation Effects in Some Systems of Partial Differential Equations ofContinuum Mechanics

数学科学：连续力学偏微分方程组中的均匀化和振荡效应

• 批准号: 8803317
• 负责人: Luc Tartar
• 金额: $ 13.87万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1991-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8803317&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Homogenization; Oscillation; Effects

The goal of this project is to study the applications to continuum mechanics of a mathematical tool developed by the principal investigator. This tool, called H theory, is an outgrowth of homogenization theory, which was also developed largely by the principal investigator. Particular areas to be studied include effective properties of mixtures, non-local effects induced by homogenization, long-time behavior of fluid interfaces, evolution of the microstructure of composite materials and nonlinear vibrations of solids.

该项目的目的是研究主要研究人员开发的数学工具连续机械的应用。 该工具称为H理论，是同质化理论的产物，该理论也主要由主要研究者开发。 要研究的特定区域包括混合物的有效特性，均质化引起的非本地效应，流体界面的长时间行为，复合材料的微观结构的演变以及固体的非线性振动。