Mathematical Sciences: Problems in Harmonic Analysis and PDE

数学科学：调和分析和偏微分方程问题

• 批准号: 9401782
• 负责人: Sagun Chanillo
• 金额: $ 3万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-11-01 至 1996-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401782&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Harmonic; Analysis

9401782 Chanillo This award supports mathematical research on problems involving systems of partial differential equations. The thrust of the work is concerned with how one uses harmonic analysis in the treatment of linear and nonlinear systems. The equations arise from several sources. One is that involving the study of rotating stars. Work will be done in establishing a bifurcation diagram for the equilibrium solutions of the free energy functional of white dwarfs. In addition, efforts will be made to understand the free boundary of the critical points of this energy function. Other work involves the rotational symmetry of partial differential equations which represent 2-dimensional fluid flow on a sphere and the analysis of where symmetry can be expected to break. Additional lines of investigation involve inverse problems from magnetohydrodynamics and local solvability problems for linear equations in the real analytic case. Partial differential equations form a basis for mathematical modeling of the physical world. The role of mathematical analysis is not so much to create the equations as it is to provide qualitative and quantitative information about the solutions. This may include answers to questions about uniqueness, smoothness and growth. In addition, analysis often develops methods for approximation of solutions and estimates on the accuracy of these approximations. ***

[401782] Chanillo该奖项支持有关偏微分方程组问题的数学研究。这项工作的重点是如何在处理线性和非线性系统时使用谐波分析。这些方程有几个来源。一个是关于旋转恒星的研究。本文将建立白矮星自由能泛函平衡解的分岔图。此外，还将努力了解该能量函数的临界点的自由边界。其他工作包括偏微分方程的旋转对称性，这些方程表示球体上的二维流体流动，并分析对称性可能在哪里被打破。另外的研究方向包括磁流体力学的逆问题和实际解析情况下线性方程的局部可解性问题。偏微分方程是物理世界数学建模的基础。数学分析的作用与其说是创建方程，不如说是提供关于解的定性和定量信息。这可能包括回答关于独特性、平滑性和增长性的问题。此外，分析常常发展出解的近似方法和对这些近似精度的估计。* * *