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

许多重要的物理现象都是用非线性偏微分方程组来模拟的。这次会议的目的是介绍一些最近发展起来的研究非线性偏微分方程解的存在性和定性行为的一般方法，特别是它将集中在偏微分方程解的振荡和非线性的竞争效应上。利用泛函分析、弱收敛和Young测度等工具，发展了补偿紧致理论，解决了连续介质力学的一些基本问题。仅用杨氏度量来研究振荡，给出了静态而非动态的描述。为了进一步了解均匀化、几何光学，并获得关于振荡传播和浓度效应的更精确的结果，Luc Tartar引入了一个二次微局域工具：H-测量。本次会议将讨论的方法旨在通过严格的数学工具回答物理学和应用数学中的基本问题。该项目将支持将于1993年6月27日至7月1日在圣克鲁斯加利福尼亚大学举行的NSF/CBMS关于补偿紧凑性、均化和H-措施的数学科学区域研究会议。该项目将支持将于1993年6月28日至7月3日在圣克鲁斯加利福尼亚大学举行的NSF-CBMS关于补偿紧凑性、均化和H-措施的数学科学区域研究会议。卡内基梅隆大学教授、法国科学院通讯委员吕克·塔塔尔将担任首席讲师。为了激发人们对数学研究的兴趣和活力，美国国家科学基金会每年都会支持一些NSF-CBMS数学科学区域研究会议。每个为期五天的会议都有一位杰出的讲师，他就一个重要的当前研究主题发表了十次演讲，该主题是数学科学中一个尖锐的重点领域。讲师随后根据这些讲座编写一份说明性专著，通常由美国数学学会或工业和应用数学学会出版，或由美国统计协会和数学统计研究所联合出版。这些会议的某些特点使其有别于典型的研究会议。它们是：(1)由领先的实践者专注于一个重要和及时的研究领域，(2)通过区域重点来持续影响和局部刺激，(3)小组审查质量、广度和及时性，以及(4)出版面向更广泛受众的专著。

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.