Mathematical Sciences: Integrable Systems in Nonlinear Dispersionless Wave Equations: The Dispersionless KP Equation

数学科学：非线性无色散波动方程中的可积系统：无色散 KP 方程

• 批准号: 8805521
• 金额: $ 3.9万
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-06-01 至 1991-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8805521&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Integrable; Systems; Nonlinear

This project is to develop a method of solving certain partial differential equations arising in the theory of hydrodynamics and aerodynamics. The particular equations deal with such phenomena as transonic flow past thin wings and the development of shock waves. Certain symmetries exist in linear PDE's via the hodograph transformation. The problem of characterizing initial data leading to global solutions is also discussed.

本课题是发展一种求解流体力学和空气动力学理论中出现的某些偏微分方程的方法。特殊的方程处理了诸如跨音速流过薄翼和激波发展等现象。通过矢状变换，线性偏微分方程存在一定的对称性。还讨论了描述导致全局解决方案的初始数据的问题。