Mathematical Sciences: Heat Equation Asymptotics with Pseudo Differential Boundary Conditions

数学科学：具有伪微分边界条件的热方程渐进

• 批准号: 9121437
• 负责人: Peter Gilkey
• 金额: $ 3.25万
• 依托单位: University of Oregon Eugene
• 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=9121437&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Heat; Equation; Asymptotics

This award will support research on heat equation asymptotics with generalized boundary conditions. The boundary conditions will be of Atiyah, Patodi, and Singer type. The research will include a study of the Dolbeault complex for a Hermitian matrix where the structures are not product near the boundary and the eta invariant of a manifold with boundary. The research supported by this award involves aspects of global analysis and spectral geometry. Global analysis attempts to relate topological properties of a space with analytic properties. Spectral geometry studies the relationship between the geometry of a space and invariants of a differential operator defined on the space.

该奖项将支持热方程研究 广义边界条件下的渐近性边界 条件将是Atiyah，Patodi和Singer类型。的 研究将包括一项对多尔博特复合体的研究， 厄米特矩阵，其中结构不是附近的乘积 边界和带边界流形的eta不变量。 该奖项支持的研究涉及以下方面： 全局分析和谱几何。全球分析尝试 将空间的拓扑性质与解析 特性.光谱几何学研究了 空间几何与微分算子不变量 定义在空间上。