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都是用非线性模型来模拟的。 偏微分方程 本次会议的目的是 提出了一些最近开发的一般技术来研究 解的存在性和定性行为 PDE的。 特别是，它将侧重于竞争的影响， 偏微分方程中的振动和非线性。 补偿紧性理论的发展是为了解决一些 连续介质力学的基本问题 泛函分析、弱收敛和Young测度。 仅通过Young测度研究振荡给出了 静态而不是动态描述。 进一步了解 均匀化，几何光学，并获得更精确的结果 关于振荡和浓度效应的传播， Tartar引入了一个二次微局部工具：H测度。 本次会议将讨论的方法旨在 回答物理和应用方面的基本问题 数学是通过严格的数学工具。 该项目将支持NSF/CBMS区域研究 数学科学会议 压实，均匀化和H-措施，将于6月27日至 1993年7月1日，在圣克鲁斯的加州大学。 这 该项目将支持一个NSF-CBMS区域研究会议， 关于补偿紧性的数学科学， 1993年6月28日至7月3日举行的均质化和H-措施， 在圣克鲁斯的加州大学。 Luc教授 卡耐基梅隆大学的塔塔和一名通讯员 法国科学院院长， 讲师。 激发数学兴趣和活动 研究，国家科学基金会每年支持一个 国家科学基金-生物多样性管理系统区域研究会议的次数 数学科学。 每次为期五天的会议都有一个 一位杰出的讲师，他就一个主题做了十次讲座， 当前重要的研究在一个尖锐的重点领域， 数学科学 讲师随后准备了一份 根据这些讲座撰写的专著，通常是 美国数学学会（American Mathematical Society） 工业和应用数学，或联合由美国 统计协会和数学研究所 统计 这些会议的某些特点使其与众不同 典型的研究会议。 （1）专注于A 一个重要而及时的研究领域， （2）持续的效果和局部刺激， 区域重点，（3）质量、广度和 及时性;（4）出版面向更广泛受众的专著。