Mathematical Sciences: Nonlinear Partial Differential Equations of Continuum and Fluid Mechanics

数学科学：连续体非线性偏微分方程和流体力学

• 批准号: 9500284
• 负责人: Thomas Sideris
• 金额: --
• 依托单位: University of California-Santa Barbara
• 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 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500284&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Nonlinear; Partial; Differential

PI: Sideris DMS-9500284 A class of isotropic, hyperelastic materials will be sought for which the corresponding equations of motion have smooth global solutions for small initial displacements. For planar, compressible, inviscid fluids, classes of initial data will be identified which delay the appearance of singularity formation. Smooth global solutions for the equations of motion for planar, inhomogeneous, incompressible, viscous fluids will be constructed. These problems have some features in common, and their analysis will require inter-related techniques. 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.

主要研究者：Sideris DMS-9500284将寻找一类各向同性超弹性材料，其相应的运动方程具有小初始位移的光滑全局解。对于平面的，可压缩的，无粘性的流体，类的初始数据将被确定延迟奇异性形成的外观。将构造平面、非均匀、不可压缩、粘性流体运动方程的光滑整体解。这些问题有一些共同的特点，他们的分析将需要相互关联的技术。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。