权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

U.S.-France Cooperative Research: Qualitative Properties inDynamics and Mathematical Physics

美法合作研究：动力学和数学物理的定性特性

基本信息

批准号：
9217469
负责人：
Jack Hale
金额：
$ 1.71万
依托单位：
Georgia Tech Research Corporation
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
1993
资助国家：
美国
起止时间：
1993-05-01 至 1996-10-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=9217469&HistoricalAwards=false
关键词：
U.S.France Cooperative Research Qualitative

项目摘要

This three-year award supports U.S.-France cooperative research in applied mathematics. The proposal involves two research groups in the U.S. and France led by Jack Hale of the Georgia Institute of Technology and Genevieve Raugel of the University of Paris, South (Orsay). The investigators propose to study the qualitative properties of infinite dimensional dynamical, physical systems. Such systems are usually described by partial differential equations (PDE) or by infinite systems of ordinary differential equations (ODE) or by maps of some infinite dimensional sets. Utilizing these methods and others related to mathematical physics and quantum systems, the investigators will investigate some concrete problems: (1) the properties of flows as defined by dissipative PDE; (2) notions of turbulence (space- time chaos), coherent structures, and intermittency in extended dynamical systems; and (3) relationships between the properties of diffusion in phase space and between the spectrum of the Schrodinger operator and repellers of dynamical systems. The Georgia Tech group approaches problems of dynamical systems through the study of ordinary differential equations and maps. They bring to this collaboration expertise in functional analysis and mathematical physics. The Orsay group consists of specialists in partial differential equations as applied to problems in dynamical systems. They are well versed in operator theory and C*-algebras. Their combined efforts will extend the theory of dynamical systems to partial differential equations.

这个为期三年的奖项支持美国-法国合作研究在应用数学中。该提案涉及两项研究由格鲁吉亚州的杰克·黑尔领导的美国和法国团体技术研究所和大学的Genevieve Raugel 位于巴黎南部（奥赛）。研究人员建议研究无限维动力学的定性性质，物理的系统. 这种系统通常由部分微分方程（PDE）或无穷常微分方程组微分方程（ODE）或通过一些无限的映射维数集利用这些方法和其他有关数学物理和量子系统，研究人员将研究了一些具体问题：（1）流的性质如耗散PDE所定义;（2）湍流（空间- 时间混沌），相干结构，并在扩展动力系统;（3）性质之间的关系扩散的相空间和光谱之间的薛定谔算子与动力系统的排斥子。格鲁吉亚技术小组研究动力学问题系统通过研究常微分方程和地图他们为这种合作带来了功能方面的专业知识，分析和数学物理。奥赛小组由偏微分方程应用于在动力系统中。他们精通算子理论 C*-代数他们的共同努力将扩展理论从动力系统到偏微分方程。