Mathematical Sciences: Analytical Approaches to Singular Perturbation Problems of Significance to Applications

数学科学：具有应用意义的奇异摄动问题的分析方法

• 批准号: 8908013
• 负责人: Robert O'Malley
• 金额: $ 9.8万
• 依托单位: Rensselaer Polytechnic Institute
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-08-01 至 1992-04-01
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8908013&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Analytical; Approaches; Singular

This research will study the asymptotic solution of nonline- ar initial and boundary value problems involving systems of differential equations. A characteristic of the solutions of these equations is that they exhibit rapid changes within thin regions. Consequently, the asymptotic methods are able to make use of the presence of multiple scales. Of particular interest in this research are problems involving boundary and interior layers. The work is motivated by physical applications including models which simulate the operation of semiconductor devices and problems arising from optimal control. Problems will be attacked using a combined analytical and numerical approach.

这项研究将研究涉及微分方程系统的非线AR初始和边界价值问题的渐近解决方案。 这些方程式的解决方案的一个特征是它们在薄区域内表现出快速变化。 因此，渐近方法能够利用多个量表的存在。 在这项研究中特别感兴趣的是涉及边界和内部层的问题。 这项工作是由物理应用激励的，包括模型，这些模型模拟了半导体设备的操作以及最佳控制引起的问题。 问题将使用组合的分析和数值方法攻击。