Mathematical Sciences: Estimates for Linear and Nonlinear Wave Equations

数学科学：线性和非线性波动方程的估计

• 批准号: 9104506
• 负责人: R. Michael Beals
• 金额: $ 8.36万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-01 至 1994-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9104506&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Estimates; Linear; Nonlinear

This project will involve nonlinear strictly hyperbolic differential equations. We will consider the following problems: estimates for linear equations, decay of solutions, and extension to nonconstant coefficients of results known for the D'Alambertian operator. The studies will include the analysis of the interaction of singularities across nonsmooth surfaces. Further construction of examples exhibiting nonlinear singularities will be attempted. Precise regularity theorems will be developed in order to show that certain explicit approximate solutions differ from the actual ones. Technological developments such as better radars, X-ray devices, and scanners ultimately rely on the understanding of the hyperbolic equations considered in this project.

这个项目将涉及到非线性严格双曲型微分方程组。我们将考虑以下问题：线性方程的估计，解的衰减，以及对已知的D‘Alambertian算子结果的非常系数的推广。这些研究将包括对非光滑表面上奇点相互作用的分析。将尝试进一步构造展示非线性奇点的例子。为了证明某些显式近似解与实际解不同，将发展精确的正则性定理。技术的发展，如更好的雷达、X射线设备和扫描仪，最终取决于对本项目中所考虑的双曲方程的理解。