Mathematical Sciences: Problems in Linear and Nonlinear WaveMotion

数学科学：线性和非线性波动问题

• 批准号: 9203413
• 负责人: Jeffrey Rauch
• 金额: $ 12.2万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1996-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9203413&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Linear; Nonlinear

The principal investigator will study a variety of problems concerning the qualitative properties of the solutions of partial differential equations which describe nonlinear wave motion. In particular, analytic justification of asymptotic methods for nonlinear waves arising in geometric optics will be sought and questions concerning the controllability of hyperbolic waves will be studied. The qualitative analysis of nonlinear waves is of significant scientific interest in view of their wide spread occurence in real world situations.

首席研究员将研究有关描述非线性波动的偏微分方程解的定性性质的各种问题。特别地，将寻求几何光学中非线性波的渐近方法的解析证明，并将研究有关双曲波的可控性的问题。鉴于非线性波在现实世界中广泛存在，对其进行定性分析具有重要的科学意义。