Mathematical Sciences: Linear and Nonlinear Hyperbolic Problems

数学科学：线性和非线性双曲问题

• 批准号: 9202361
• 负责人: Antonio Sa Barreto
• 金额: $ 6万
• 依托单位: Purdue Research Foundation
• 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 1995-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9202361&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Linear; Nonlinear; Hyperbolic

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, an investigation will be made of the propagation of singularities of solutions along caustics and to study linear inverse hyperbolic problems like determining the speed of sound from information given by the problem. The qualitative analysis of nonlinear waves is of significant scientific interest in view of their wide spread occurrence 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，我们将研究解的奇异性沿焦散线的传播，并研究线性逆双曲问题，如根据问题给出的信息确定声速。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。