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.

主要研究者将研究弱非线性波。 主要目标是了解小非线性的共振影响。 数学方程式建模物理现象，例如声波或水波或梁的弹性弯曲，例如结构通常会忽略小的非线性项，这些术语可能会在内部共振引起的长时间尺度上产生积累的效果。 鉴于在现实世界中这种现象的广泛传播，非线性波的定性和数值分析具有重大的科学兴趣。