Mathematical Sciences: Singular Perturbations in Applied Mathematics: Methods and Applications

数学科学：应用数学中的奇异扰动：方法与应用

• 批准号: 8703011
• 负责人: Bernard Matkowsky
• 金额: $ 21.98万
• 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=8703011&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Singular; Perturbations; Applied

This research will develop and apply new singular perturbation methods to boundary value problems for nonlinear ordinary differential equations and for partial integro-differential-difference equations. The results will enable us to calculate the stationary distribution of fluctuations about, and the rate of transitions from (deterministically) stable states of dynamical systems subject to noise. Stochastic integro-differential-difference equations and their associated forward and backward Kolmogorov equations will also be analyzed. The research will have direct applications to a variety of problems in science and engineering. Among them are computer performance evaluation, customer service queue arrangements, chemical physics, noise induced transitions between stable configurations of a dynamical system, etc.

本研究将发展和应用新的奇异摄动方法来求解非线性常微分方程边值问题和偏积分-微分-差分方程组的边值问题。这些结果将使我们能够计算受噪声影响的动力系统的涨落的平稳分布，以及从(确定性的)稳定状态的转变速率。还将分析随机积分-微分-差分方程组及其相关的前向和后向Kolmogorov方程。这项研究将直接应用于科学和工程中的各种问题。其中包括计算机性能评估、客户服务队列安排、化学物理、动力系统稳定构型之间的噪声诱导转换等。