Mathematical Sciences: Microlocal Measures and the Study of Oscillations, Concentration Effects and Comparison Mechanics in Nonlinear Partial Differential Equations

数学科学：非线性偏微分方程中的微观局部测度和振荡、浓度效应和比较机制的研究

• 批准号: 9401310
• 负责人: Luc Tartar
• 金额: $ 15万
• 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: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401310&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Microlocal; Measures; Study

9401310 Tartar In the last twenty years, the Principal Investigator has pioneered the creation of most of the new mathematical tools which are now used for studying microstructures appearing in the (usually nonlinear partial differential equations of Continuum Mechanics or Physics: Homogenization, Compensated Compactness, H-measures. The present Proposal deals with research of a theoretical nature, with the purposes of unifying many fragmentary results and of creating a still more powerful tool. It links questions of Classical Analysis on one side to the description of microstructures observed in existing materials on the other side, one important application being to devise new materials whose microstructure creates some improved properties over existing materials. In the last twenty years, the Principal Investigator has pioneered the creation of most of the new mathematical tools which are now used for studying the microstructures appearing in important situations in Material Sciences and Engineering. This Proposal deals with theoretical questions which can help describing how to devise new materials whose structure at a fine level is responsible for improved properties over existing materials.

9401310 鞑靼 在过去的二十年里，首席研究员率先创建了大多数新的数学工具，这些工具现在用于研究出现在（通常是连续体力学或物理学的非线性偏微分方程：均匀化、补偿紧致性、H -措施。本提案涉及理论性质的研究，目的是统一许多零散的结果并创建一个更强大的工具。一方面是经典分析的问题，另一方面是对现有材料中观察到的微观结构的描述，一个重要的应用是设计新材料，其微观结构比现有材料具有一些改进的性能，在过去的二十年中，首席研究员开创了先河。大多数新数学工具的创建现在用于研究材料科学和工程中重要情况下出现的微观结构。该提案涉及理论问题，有助于描述如何设计新材料，其精细结构可改善现有材料的性能。