Mathematical Sciences: Microlocal Analysis and Nonlinear Waves

数学科学：微局域分析和非线性波

• 批准号: 9104057
• 负责人: Mark Williams
• 金额: $ 10.05万
• 依托单位: University of North Carolina at Chapel Hill
• 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: 1991-06-01 至 1995-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9104057&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Microlocal; Analysis; Nonlinear

This project involves the use and development of microlocal techniques to study three categories of nonlinear wave phenomena: diffraction by smooth obstacles, diffraction by nonsmooth obstacles, and transmission from one medium to another. In all three cases we are concerned with the behavior of singularity- bearing rays as well as with progressing waves. The aim is to produce propagation of regularity theorems along with examples demonstrating the optimality of those theorems. In the latter two categories, the research addresses some basic questions concerning existence which remain open even in the linear case.

该项目涉及使用和开发微本地 技术来研究三类非线性波现象： 光滑障碍物绕射，非光滑障碍物绕射 障碍，以及从一种媒介到另一种媒介的传播。 在所有 我们关注的三种情况是奇点的行为 带有射线和前进波。 目的是 产生正则性定理的传播沿着例子 证明这些定理的最优性。 在后一 两类，研究解决了一些基本问题， 关于存在，即使在线性情况下也是开放的。