Mathematical Sciences: Research in Differential Equations

数学科学：微分方程研究

• 批准号: 9302737
• 负责人: Stuart Hastings
• 金额: $ 6.5万
• 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: 1993
• 资助国家: 美国
• 起止时间: 1993-07-15 至 1995-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9302737&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Differential; Equations

9302737 Hastings This project concerns investigations into mathematical problems of nonlinear ordinary differential equations. There are six areas under investigation. They include asymptotics and painleve transcendents involving solutions obtained by inverse scattering, shooting methods applied to the study of chaos, specially in the analysis of Lorenz equations, and self-similar solutions of Barenblatt's fourth order model for the decay of turbulent bursts. Work will also be done expanding recent studies of stability in modeling solid state diffusion in semiconductors, asymptotics beyond all orders in fifth order equations and on the smoothing of Stokes discontinuities in the asymptotic expansions of analytic functions. 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. ***

小行星9302737 本计画研究非线性常微分方程式之数学问题。 有六个领域正在调查中。 它们包括渐近性和painleve超越涉及的解决方案获得的逆散射，射击方法应用于混沌的研究，特别是在分析洛伦兹方程，和自相似的解决方案巴伦布拉特的四阶模型的湍流爆发的衰减。 工作也将完成扩展最近的研究在半导体中的固态扩散建模的稳定性，超越所有订单的五阶方程的渐近性和平滑的斯托克斯不连续性的渐近展开的解析函数。 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。 ***