Blowup analysis for two dimensional elliptic equations with exponential nonlinearities

具有指数非线性的二维椭圆方程的爆炸分析

• 批准号: 0600275
• 负责人: Lei Zhang
• 金额: $ 8.58万
• 依托单位: University of Florida
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-06-01 至 2008-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0600275&HistoricalAwards=false
• 关键词: Blowup; analysis; two; dimensional; elliptic

Blowup Analysis for two-dimensional Elliptic Equations withExponential NonlinearitiesAbstract of Proposed ResearchLei Zhang This project is to study some highly nonlinear elliptic equations related to problems in geometry and physics. These equations have some very singular terms and their solutions also are quite singular. This research is to try to describe the nature of the singularities of the solutions precisely and will require the application of a many deep results from recent studies of non-linear equations. The descriptions of the singularities of these equations is likely to be quite important for physics and will help provide a geometrical and analytical understanding of the associated field theories. Similar equations also arise in some models of biological phenomena and these descriptions may be useful there.

具有指数非线性项的二维椭圆型方程的爆破分析--拟研究摘要 本项目主要研究一些与几何和物理问题相关的高度非线性椭圆型方程。这些方程有一些非常奇异的项，其解也是非常奇异的。这项研究试图精确地描述解的奇异性的性质，并且需要应用最近对非线性方程的研究中的许多深入结果。对这些方程奇点的描述可能对物理学非常重要，并将有助于提供对相关场论的几何和分析理解。类似的方程也出现在一些生物现象的模型中，这些描述可能在那里有用。