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.

本研究将研究涉及微分方程组的非线性初始和边值问题的渐近解。 这些方程的解的一个特点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尺度的存在。 这项研究特别感兴趣的是涉及边界层和内部层的问题。 这项工作的动机是物理应用，包括模拟半导体器件运行的模型和最优控制产生的问题。 将使用分析和数值相结合的方法来解决问题。