Mathematical Sciences: Harmonic Analysis and Partial Differential Equations

数学科学：调和分析和偏微分方程

• 批准号: 9500725
• 负责人: Carlos Kenig
• 金额: $ 43.79万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 2001-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500725&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Harmonic; Analysis; Partial

PI: Kenig DMS-9500725 Kenig will continue his research on the development of various aspects of harmonic analysis and theory application to partial differential equations. The main emphasis will be on the study of boundary value problems under minimal smoothness conditions, boundary unique continuation and the "big-bang" property of control theory, regularity of two-phase free boundary problems, and the well-posedness of nonlinear equations and systems arising in wave propagation. The necessary harmonic analysis methods for the study of these problems will be investigated concurrently. 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.

Kenig将继续研究谐波分析和偏微分方程理论应用的各个方面的发展。重点将放在最小平滑条件下的边值问题、边界唯一延拓和控制论的“大爆炸”性质、两相自由边界问题的正则性以及波传播中非线性方程和系统的适定性研究上。研究这些问题所必需的谐波分析方法将同时进行研究。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。