Mathematical Sciences: NSF/CBMS Regional Conference in Mathematical Sciences- "Compensated Compactness, Homogenization and H-Measures" June 28-July 3,1993

数学科学：NSF/CBMS 数学科学区域会议 - “补偿紧性、均质化和 H 测量” 1993 年 6 月 28 日至 7 月 3 日

• 批准号: 9215004
• 负责人: Maria Schonbek
• 金额: $ 2.5万
• 依托单位: University of California-Santa Cruz
• 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: 1993-01-01 至 1993-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9215004&HistoricalAwards=false
• 关键词: Mathematical; Sciences; NSF; CBMS; Regional

Many important physical phenomena are modelled by nonlinear partial differential equations. The aim of this conference is to present some general techniques recently developed to study existence and qualitative behaviour of solutions to nonlinear PDE's. In particular it will focus on competing effects of oscillations and nonlinearity in partial differential equations. The theory of compensated compactness was developed to solve some fundamental problems of continuum mechanics using tools of functional analysis, weak convergence and Young measures. Studying oscillations solely by means of Young measures gave a static and not a dynamic description. To further understand homogenization, geometric optics and obtain more precise results on propagation of oscillations and concentrations effects, Luc Tartar introduced a quadratic microlocal tool: the H-measures. The methods that will be discussed in this conference are aimed to answer basic questions aring in physics and applied mathematics by means of rigorous mathematical tools. This project will support an NSF/CBMS Regional Research Conference in the Mathematical Sciences on Compensated Compactness, Homogenization and H-Measures, to be held June 27 to July 1, 1993, at the University of California, Santa Cruz. This project will support an NSF-CBMS Regional Research Conference in the Mathematical Sciences on Compensated Compactness, Homogenization and H-Measures to be held June 28 - July 3, 1993, at the University of California, Santa Cruz. Professor Luc Tartar of Carnegie Mellon University and a corresponding member of the French Academy of Sciences, will be the principal lecturer. To stimulate interest and activity in mathematical research, the National Science Foundation each year supports a number of NSF-CBMS Regional Research Conferences in the Mathematical Sciences. Each five-day conference features a distinguished lecturer who delivers ten lectures on a topic on important current research in one sharply focused area of the mathematical sciences. The lecturer subsequently prepares an expository monograph based upon these lectures, which is normally published by the American Mathematical Society or the Society for Industrial and Applied Mathematics, or jointly by the American Statistical Association and the Institute of Mathematical Statistics. Certain features differentiate these conferences from typical research conferences. These are: (1) Focus on a single important and timely area of research by a leading practitioner, (2) Continued effect and local stimulation through regional emphasis, (3) Panel review for quality, breadth, and timeliness, and (4) Published monographs for a wider audience.

许多重要的物理现象是由非线性偏微分方程建模的。 这次会议的目的是介绍最近开发的一些通用技术来研究非线性PDE的解决方案的存在和定性行为。 特别是，它将集中在偏微分方程中振荡和非线性的竞争效果上。 为了使用功能分析，弱收敛和年轻措施的工具解决连续机械的一些基本问题，开发了补偿紧凑性的理论。 仅通过年轻措施研究振荡给出了静态而不是动态描述。 为了进一步了解均质化，几何光学器件并获得了振荡和浓度效应的传播的更精确的结果，Luc Tartar引入了二次微局部工具：H测量。 将在本次会议中讨论的方法旨在通过严格的数学工具来回答物理和应用数学的基本问题。 该项目将在1993年6月27日至1993年7月1日在加利福尼亚大学圣克鲁斯分校举行，支持关于补偿紧凑，同质化和H-措施的数学科学的NSF/CBMS区域研究会议。 该项目将在1993年6月28日至7月3日在加利福尼亚大学圣克鲁斯分校举行的有关紧凑，均质化和H-测量的数学科学上的NSF-CBMS区域研究会议。 卡内基·梅隆大学（Carnegie Mellon University）的卢克塔塔尔（Luc Tartar）教授和法国科学学院的相应成员将是主要讲师。 为了激发数学研究的兴趣和活动，国家科学基金会每年都支持数学科学中的许多NSF-CBMS区域研究会议。 每个为期五天的会议都有一位杰出的讲师，他在数学科学的一个备受关注的领域中就重要的当前研究主题发表了十个讲座。 讲师随后根据这些讲座准备了一个说明性专着，该讲座通常由美国数学学会或工业和应用数学学会或美国统计协会和数学统计研究所共同发表。 某些特征将这些会议与典型的研究会议区分开。 这些是：（1）专注于领先从业者的一个重要及时的研究领域，（2）通过区域强调持续效应和局部刺激，（3）小组审查质量，广度和及时性，以及（4）为更多观众出版了专着。