Mathematical Sciences: Singularities in Determined AnalyticPDE and Associated Qualitative Properties of Solutions

数学科学：确定的解析偏微分方程中的奇点以及解的相关定性性质

• 批准号: 9123752
• 负责人: Marek Kossowski
• 金额: $ 2.65万
• 依托单位: University of South Carolina at Columbia
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-06-15 至 1995-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9123752&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Singularities; Determined; AnalyticPDE

The principal investigator will study the singularities in low dimensional non-linear real analytic partial differential equations. A key feature of his approach will be the use of multivalued solutions and a geometric approach to the study of singularities. A general objective of the research will be to identify geometric invariants of partial differential equations which control singularities of solutions. This award will support research in the general area of differential geometry and global analysis. Differential geometry is the study of the relationship between the geometry of a space and analytic concepts defined on the space. Global analysis is the study of the overall geometric and topological properties of a space by piecing together local information. Applications of these areas of mathematics in other sciences include the structure of complicated molecules, liquid-gas boundaries, and the large scale structure of the universe.

首席研究员将研究低维非线性实解析偏微分方程中的奇点。他的方法的一个关键特征是使用多值解决方案和几何方法来研究奇点。研究的总体目标是确定控制解奇点的偏微分方程的几何不变量。 该奖项将支持微分几何和全局分析一般领域的研究。微分几何是研究空间几何形状与空间上定义的解析概念之间关系的学科。全局分析是通过拼凑局部信息来研究空间的整体几何和拓扑特性。这些数学领域在其他科学中的应用包括复杂分子的结构、液气边界和宇宙的大尺度结构。