Mathematical Sciences: Singularly Perturbed Integral Equations and Applications

数学科学：奇异摄动积分方程及其应用

• 批准号: 8700962
• 负责人: W. Edward Olmstead
• 金额: $ 10.05万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-01 至 1990-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8700962&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Singularly; Perturbed; Integral

This research program is concerned with the analysis of various physical problems whose mathematical formulation involves a singularly perturbed integral equation. It will focus on (1) the development of systematic methods for obtaining an asymptotic solution to such problems, and (2) the application of the new methodology to a variety of relevant problems in science and engineering. The research results will have an impact in technical areas such as thermal and chemical diffusion, combustion, mechanical vibrations, epidemiology and some electronic devices.

这个研究项目涉及各种物理问题的分析，这些问题的数学表述涉及一个奇异摄动的积分方程式。它将集中于(1)发展获得此类问题的渐近解的系统方法，以及(2)将新方法应用于科学和工程中的各种相关问题。研究成果将对热和化学扩散、燃烧、机械振动、流行病学和一些电子设备等技术领域产生影响。