Mathematical Sciences: Resonance in Weakly Nonlinear Hyperbolic Partial Differential Equations

数学科学：弱非线性双曲偏微分方程中的共振

• 批准号: 9205916
• 负责人: David Bosley
• 金额: $ 6万
• 依托单位: Harvey Mudd College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-15 至 1994-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9205916&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Resonance; Weakly; Nonlinear

The principal investigator will study weakly nonlinear waves. The main objective will be to understand the resonance effects of small nonlinearities. Mathematical equations modelling physical phenomena such as acoustic or water waves or elastic bending of beam like structures oftentimes ignore small nonlinear terms which may have accumulative effects over long time scales due to internal resonances. The qualitative and numerical analysis of nonlinear waves is of significant scientific interest in view of the wide spread occurrence of such phenomena in real world situations.

首席研究员将研究弱非线性波。 主要目标是了解小非线性的共振效应。 对声波或水波或梁状结构的弹性弯曲等物理现象进行建模的数学方程经常忽略小的非线性项，这些非线性项可能由于内部共振而在长时间尺度上产生累积效应。 鉴于这种现象在现实世界中广泛发生，非线性波的定性和数值分析具有重要的科学意义。