Mathematical Sciences: Variational Methods and Applications

数学科学：变分方法及其应用

• 批准号: 8901477
• 负责人: Giles Auchmuty
• 金额: $ 8.4万
• 依托单位: University of Houston
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-01 至 1993-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8901477&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Variational; Methods; Applications

8901477 Auchmuty The principal investigator will conduct research on the construction and analysis of variational principles for certain problems that are important in applications. He will develop, and implement, some new algorithms for numerically solving these variational problems. The problems to be studied include non-self-adjoint elliptic eigenproblems and their application to linear hydrodynamic stability theory, and nonlinear eigenvalue problems for the Hartree and Hartree-Fock equations which arise in quantum theory. Another class of problems centers on the variational characterization of solutions of the Navier-Stokes equations, including the properties and consequences of these principles. The numerical research will center on numerical methods for finding eigenvalues and eigenvectors of both symmetric and non-symmetric matrices, also the numerical simulation of the equilibria of rotating self-gravitating fluids, which are simple hydrodynamical models of stars and planets.

8901477 奥赫穆蒂 首席研究员将对 变分原理的构造与分析 这些问题在应用中很重要。 他会发展， 并实现了一些新的数值求解算法 这些变分问题。 要研究的问题包括非自伴 椭圆特征值问题及其在线性 水动力稳定性理论和非线性特征值 Hartree和Hartree-Fock方程的问题， 在量子理论中。 另一类问题集中在 Navier-Stokes方程解的变分特征 方程，包括这些方程的性质和后果， 原则 数值研究将以数值计算为中心， 求特征值和特征向量的方法 对称和非对称矩阵，以及数值 旋转自引力平衡的模拟 流体，这是简单的恒星流体动力学模型， 星球