Mathematical Sciences: Quasiconformal Analysis: Extensions and Applications

数学科学：拟共形分析：扩展和应用

• 批准号: 9501561
• 负责人: Juan Manfredi
• 金额: $ 8.58万
• 依托单位: University of Pittsburgh
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9501561&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Quasiconformal; Analysis; Extensions

PI: Manfredi DMS-9501561 Manfredi will investigate the interplay between nonlinear elasticity and function theory. He will attempt to bridge the gap between quasiregular mappings and mappings describing deformations of certain types of hyperelastic materials. Regularity up to the boundary of solutions to nonlinear elliptic systems that appear often in applications to non-Newtonian fluid mechanics will also be discussed. The significance of this research is the interconnections between areas of classical analysis and materials science. Partial differential equations form a basis for mathematical modeling of the physical world. The role of mathematical analysis is not so much to create the equations as it is to provide qualitative and quantitative information about the solutions. This may include answers to questions about uniqueness, smoothness and growth. In addition, analysis often develops methods for approximation of solutions and estimates on the accuracy of these approximations.

PI：Manfredi DMS-9501561 曼弗雷迪将研究非线性弹性和函数理论之间的相互作用。 他将试图弥合准正则映射和映射之间的差距差距描述某些类型的超弹性材料的变形。 经常出现在非牛顿流体力学的应用中的非线性椭圆系统的解的边界的正则性也将被讨论。 这项研究的意义在于经典分析和材料科学领域之间的相互联系。 偏微分方程是物理世界数学建模的基础。 数学分析的作用与其说是建立方程，不如说是提供关于解的定性和定量信息。 这可能包括关于独特性，平滑性和增长的问题的答案。 此外，分析经常发展出解的近似方法和对这些近似的准确性的估计。