Mathematical Sciences: Variational Methods and Applications

数学科学：变分方法及其应用

• 批准号: 8701886
• 负责人: Giles Auchmuty
• 金额: $ 4.52万
• 依托单位: University of Houston
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-08-01 至 1990-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701886&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Variational; Methods; Applications

The investigator proposes to develop and analyze variational principles for various problems that arise in mechanics and in chemical systems theory. He also proposes to develop algorithms and numerical methods for approximating the solutions of these problems. Particular attention will be devoted to the variational characterization of the solutions of the Navier-Stokes equations, the initial value problem for pipe flow and of various problems in hydrodynamic stability. It is also planned to study certain second order equations including equations from mechanics and certain wave equations and various eigenvalue problems. Variational methods of the type proposed here have numerous applications in computational methods in engineering and other sciences.

研究人员建议开发和分析变 在力学和物理学中出现的各种问题的原理， 化学系统理论 他还建议开发算法 和数值方法近似的解决方案，这些 问题 特别注意将致力于变 Navier-Stokes方程解的特征， 管流的初值问题和各种问题， 流体动力稳定性 还计划研究某些第二 阶方程包括力学方程和某些波动方程 方程和各种特征值问题。 这里提出的类型的变分方法有许多 在工程和其他计算方法中的应用 以理工科为重