Advances in the theory of dispersive equations

色散方程理论的进展

• 批准号: 0602678
• 负责人: Gigliola Staffilani
• 金额: --
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2010-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0602678&HistoricalAwards=false
• 关键词: Advances; theory; dispersive; equations

Advances in the Theory of Dispersive Equations Abstract of Proposed ResearchGigliola Staffilani This project is to study the well posedness of dispersive partial differential equations, with particular emphasis on the nonlinear Schroedinger equation. That is, how much regularity must one impose on the initial data to insure existence and uniqueness of the solutions at later times? Also what regularity is preserved and what is the asymptotic behavior of the solutions? Recent advances in the theory of nonlinear dispersive equations have been driven by the introduction of sophisticated methods and new techniques from Fourier and harmonic analysis. This proposal is to further pursue these new directions and to better understand their implications.

分散方程理论的进步摘要拟议的研究gigliola sterfilani这个项目是研究分散偏微分方程的良好姿势，特别强调了非线性schroedinger方程。也就是说，必须对初始数据强加多少规律性，以确保以后的解决方案的存在和独特性？另外，保留什么规律性？解决方案的渐近行为是什么？非线性分散方程理论的最新进展是由从傅立叶和谐波分析中引入复杂方法和新技术的驱动的。 该建议是进一步追求这些新的方向，并更好地理解它们的含义。