Mathematical Sciences: The Differential Geometry of PartialDifferential Equations

数学科学：偏微分方程的微分几何

• 批准号: 9505125
• 负责人: Robert Bryant
• 金额: $ 13.5万
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9505125&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Differential; Geometry; PartialDifferential

9505125 Bryant The proposed research lies in the area of exterior differential systems. The proposer seeks to classify systems of various types which admit non-trivial conservation laws, and to develop effective algorithms for computing integrable extensions of a given system. The proposer also wishes to understand the geometric invariants of a control system and to investigate control algorithms. The main tools to be used are Cartan's method of equivalence and Cartan-Kahler theory. Exterior differential systems generalize systems of partial differential equations; their study is heavily geometric and heavily computational at the same time. Control theory is used extensively in such areas as manufacturing and robotics; the proposed research may help to create more efficient design algorithms based upon a deeper understanding of the geometric invariants involved.

小行星9505125 建议的研究在于外微分系统的领域。提议者试图对承认非平凡守恒律的各种类型的系统进行分类，并开发有效的算法来计算给定系统的可积扩展。提出者还希望了解控制系统的几何不变量，并研究控制算法。使用的主要工具是Cartan的等效方法和Cartan-Kahler理论。 外微分系统是偏微分方程系统的推广;它们的研究是大量的几何和大量的计算在同一时间。控制理论被广泛用于制造和机器人等领域;所提出的研究可能有助于基于对所涉及的几何不变量的更深入理解来创建更有效的设计算法。