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; 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 Manfredi将研究非线性弹性和功能理论之间的相互作用。 他将试图弥合准映射映射和描述某些类型超弹性材料的变形的映射之间的差距。 还将讨论在非线性椭圆系统到非线性椭圆系统边界的规律性，这些椭圆系统经常出现在非牛顿流体力学中。 这项研究的意义是经典分析和材料科学领域之间的互连。 部分微分方程构成了物理世界数学建模的基础。 数学分析的作用并不是创建方程，而是提供有关解决方案的定性和定量信息。 这可能包括有关独特性，光滑和成长的问题的答案。 此外，分析通常会开发出解决这些近似值准确性的解决方案和估计值的方法。