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.

非线性色散方程的极其重要的应用范围从凝聚态到非线性和激光光学，其数学研究已有 100 多年的历史。即便如此，许多基本的数学问题——包括适定性——直到最近几年才得到严格解决。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打开了大门。 加州大学洛杉矶分校的陶教授在调和分析在科特韦格德弗里斯方程、非线性薛定谔方程和波动图等相关领域的应用方面做出了开创性的贡献。陶教授将带来一系列10在拉斯克鲁塞斯新墨西哥州立大学举办题为“非线性色散和波动方程”的讲座。虽然陶和其他人提出的技术相当新，并且仍然具有新应用的巨大潜力，但许多关键思想现在可以被视为“原则”。这些都会在陶老师的讲座中阐述。还将讨论现阶段的一些主要应用以及尚未解决的问题。任何从事调和分析、偏微分方程或波传播数学物理的人，无论是老手还是新手，都应该对这些讲座感兴趣。