Mathematical Sciences: Partial Differential Equations in Nonsmooth Domains

数学科学：非光滑域中的偏微分方程

• 批准号: 9201208
• 负责人: Zhongwei Shen
• 金额: $ 3.5万
• 依托单位: Purdue Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-08-01 至 1995-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9201208&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Partial; Differential; Equations

The mathematical work supported by this grant lies in the area of systems of partial differential equations. More specifically, boundary value problems in domains with nonsmooth boundaries for elliptic and parabolic systems and higher order equations will be investigated. In addition work on homogenization will be carried out. One of the particular problems of interest involves elliptic systems of elastostatics and parabolic systems with boundary data in the Lebesgue spaces. It is not known, in dimension four and greater, what range of power norms of boundary data will yield solutions. Partial differential equations form the backbone of mathematical modeling in the physical sciences. Phenomena which involve continuous change such as that seen in motion, materials and energy are known to obey certain general laws which are expressible in terms of the interactions and relationships between partial derivatives. The key role of mathematics is not to state the relationships, but rather, to extract qualitative and quantitative meaning from them.

这项资助支持的数学工作在于 偏微分方程组 更 具体地说，非光滑区域中的边值问题 椭圆型和抛物型方程组的边界及高阶 方程将被研究。 此外， 进行均质化。 其中一个特别的 感兴趣的问题涉及弹性静力学的椭圆系统 和抛物型方程组的边界数据在Lebesgue空间。 目前还不知道，在第四维和更大的维度中， 边界数据的幂范数将产生解。 偏微分方程是 物理科学中的数学建模。 的现象 包括连续变化，如运动、材料 和能量都服从某些普遍规律， 可以用相互作用和关系来表达 偏导数之间的关系 数学的关键作用不是 来陈述这些关系，而是为了提取定性的 和量化的意义。