Harmonic Analysis and PDE

调和分析和偏微分方程

• 批准号: 0855541
• 负责人: Sagun Chanillo
• 金额: $ 18.7万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-08-15 至 2014-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0855541&HistoricalAwards=false
• 关键词: Harmonic; Analysis; PDE

The project considers various problems in the area of partial differential equations, including free boundary problems, variational problems, and geometric problems. These problems have been chosen because they are not technical and confined to narrow areas but are interdisciplinary in spirit. For example, the problems on composite materials are derived from engineering questions. As the principal investigator has done in the past and expects to continue to do now, he will rely for the resolution of these problems on techniques and tools from several areas of mathematics (e.g., partial differential equations, geometry, the calculus of variations, mathematical physics). Some of the problems under investigation are also amenable to numerical simulation. This, the principal investigator hopes, will provide additional insight.The chief impact of this project on areas outside of mathematics lies in the set of problems that focus on the design of composite materials. Lightweight and strong composites are playing increasingly important roles in fields such as aerospace engineering, medicine, etc. Theoretical studies like those to be undertaken in this project, in which one tries to maximize rigidity, should furnish valuable insight into the fabrication of such smart materials. There could, of course, be other areas of application. For instance, a survey of the literature reveals that the principal investigator's earlier work on composites has found use in ecological studies.

该项目考虑了偏微分方程领域的各种问题，包括自由边界问题，变分问题和几何问题。之所以选择这些问题，是因为它们不是技术性的，也不局限于狭窄的领域，而是精神上的跨学科。例如，复合材料的问题是从工程问题中衍生出来的。正如首席研究员在过去所做的，并希望继续做现在，他将依赖于解决这些问题的技术和工具，从几个领域的数学（例如，偏微分方程、几何、变分法、数学物理）。一些调查中的问题也服从数值模拟。首席研究员希望，这将提供更多的见解。该项目对数学以外领域的主要影响在于一系列专注于复合材料设计的问题。轻质和坚固的复合材料在航空航天工程，医学等领域中发挥着越来越重要的作用。在这个项目中，人们试图最大限度地提高刚度，因此应该对这种智能材料的制造提供有价值的见解。当然，还可以有其他应用领域。例如，对文献的调查显示，首席研究员关于复合材料的早期工作已经在生态学研究中得到了应用。