Analytical Approaches to Singular Perturbation Problems of Significance in Applications

具有应用意义的奇异摄动问题的分析方法

• 批准号: 0103632
• 负责人: Robert O'Malley
• 金额: $ 10.2万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-08-15 至 2005-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0103632&HistoricalAwards=false
• 关键词: Analytical; Approaches; Singular; Perturbation; Problems

NSF Award Abstract - DMS-0103632Mathematical Sciences: Analytical Approaches to Singular Perturbation Problems of Significance in Applications0103632O'MalleyThe research will develop asymptotic methods to solve nonlinear singularly perturbed boundary value problems for both ordinary and partial differential equations. A special emphasis will be the systematic development of renormalization methods, which theoretical physicists have proposed as a unified tool for asymptotic analysis. Another will be continued investigation of metastable dynamics for algebraic, as well as exponential, asymptotics. The problems are related since they both deal with long-time asymptotics and the classical method of multiple scales.Asymptotic methods, like computation, provide an important way to find approximate solutions to nonlinear problems arising in significant applications. This work seeks to further develop such analytical techniques and to apply them in engineering and the sciences.

NSF奖摘要-DMS -0103632数学科学：应用程序中具有重要意义的单一扰动问题的分析方法。0103632O'MalleyTheMalleythe研究将开发渐近方法，以解决普通和部分微分方程的非线性奇异扰动边界价值问题。 特殊重点将是重新归一化方法的系统发展，理论物理学家认为这是渐近分析的统一工具。 另一个将继续研究代数和指数渐近造物的亚稳态动力学。这些问题是相关的，因为它们都处理长期渐近学和多个量表的经典方法。诸如计算之类的方法为寻找在重要应用中引起的非线性问题的近似解决方案提供了一种重要方法。 这项工作旨在进一步开发这种分析技术，并将其应用于工程和科学。