Mathematical Sciences: Shock Waves and Conservation Laws

数学科学：冲击波和守恒定律

• 批准号: 9206631
• 负责人: John Temple
• 金额: $ 9.3万
• 依托单位: University of California-Davis
• 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=9206631&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Shock; Waves; Conservation

The principal investigator will conduct research in the area of nonlinear conservation laws and shock waves, continuing the study of elementary waves and the Riemann problem in resonant nonlinear systems as well as the convergence properties of numerical methods utilizing this construction. Shock waves are the observed in many "flow" situations. The presence of steep gradients leads to serious difficulties in both theoretical and numerical methods for obtaining solutions. The qualitative and quatitative analysis of nonlinear waves is of significant scientific interest in view of the wide spread occurrence of such phenomena in real world situations.

主要研究员将在非线性守恒定律和激波领域进行研究，继续研究基本波和共振非线性系统中的黎曼问题，以及利用该结构的数值方法的收敛性。冲击波是在许多“流动”情况下观察到的。陡梯度的存在导致了理论和数值方法求解的严重困难。非线性波的定性和定量分析具有重要的科学意义，因为这种现象在现实世界中广泛存在。