Mathematical Sciences: Semilinear Partial Differential Equations and Systems

数学科学：半线性偏微分方程和系统

• 批准号: 9101446
• 负责人: Wei-Ming Ni
• 金额: $ 12.04万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-08-01 至 1995-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9101446&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Semilinear; Partial; Differential

This project will consider spiky behavior of the least energy solution of a semilinear problem in pattern formation, classification of solutions of the conformal curvature equations, symmetry of positive solutions of semilinear elliptic equations, and stability of steady states for a class of semilinear heat equations. The problems to be addressed are state of the art mathematical questions motivated by problems in a wide range of scientific areas including differential geometry, developmental biology, and astronomy.

这个项目将考虑模式形成中半线性问题的最小能量解的尖峰行为，共形曲率方程的解的分类，半线性椭圆型方程正解的对称性，以及一类半线性热方程的稳态稳定性。要解决的问题是由包括微分几何、发育生物学和天文学在内的广泛科学领域的问题所驱动的最先进的数学问题。