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 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创建一个更强大的工具，它将经典分析的问题与另一侧的现有材料中观察到的微观结构相关联，一个重要的应用是设计新材料，其微观结构在过去的二十年中创造了对现有材料的一些改进的新材料。 工程。该建议涉及理论问题，这些问题可以帮助描述如何设计新材料，这些新材料的结构良好，负责改善现有材料的特性。