NSF/CBMS Regional Conference in the Mathematical Sciences: Nonlinear Dispersive and Wave Equations

NSF/CBMS 数学科学区域会议：非线性色散和波动方程

• 批准号: 0440945
• 负责人: Joseph Lakey
• 金额: $ 3.13万
• 依托单位: New Mexico State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-05-01 至 2006-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0440945&HistoricalAwards=false
• 关键词: NSF; CBMS; Regional; Conference; Mathematical

Immensely important applications of nonlinear dispersive equations range from condensed matter to non-linear and laser optics, and their mathematical study dates to well over 100 years. Even so, many fundamental mathematical questions - including well-posedness - have been rigorously addressed only in the last few years. During this time, new techniques and break-through ideas, largely from harmonic analysis, have opened the door to the resolution of such problems. Professor Terence Tao of the University of California, Los Angeles has made ground-breaking contributions in the applications of harmonic analysis to the related areas of the Korteweg de Vries equation, nonlinear Schroedinger equations, and wave maps.Professor Tao will deliver a series of 10 lectures entitled "Nonlinear Dispersive and Wave Equations" at New Mexico State University in Las Cruces. While the techniques due to Tao and others are fairly new and still hold tremendous potential for new applications, a number of the key ideas can now be deemed `principles'. These will be laid out in Tao's lectures. Some of the main applications to this stage, as well as open problems, will also be discussed. The lectures should be of interest to anyone working in harmonic analysis, partial differential equations, or the mathematical physics of wave propagation, veterans and newcomers alike.

非线性分散方程的极其重要的应用范围从凝结物质到非线性和激光光学，其数学研究的历史可以追溯到100多年。即便如此，仅在过去几年中，许多基本的数学问题（包括适应性的问题）一直受到严格解决。在此期间，主要来自谐波分析的新技术和突破性想法为解决此类问题的解决打开了大门。 Professor Terence Tao of the University of California, Los Angeles has made ground-breaking contributions in the applications of harmonic analysis to the related areas of the Korteweg de Vries equation, nonlinear Schroedinger equations, and wave maps.Professor Tao will deliver a series of 10 lectures entitled "Nonlinear Dispersive and Wave Equations" at New Mexico State University in Las Cruces.尽管TAO和其他人引起的技术是相当新的，并且仍然具有新应用的巨大潜力，但现在可以将许多关键思想视为“原理”。这些将在陶的讲座中布置。还将讨论此阶段的一些主要应用以及开放问题。从事谐波分析，部分微分方程或波浪传播，退伍军人和新移民的数学物理学的任何人都应该感兴趣。