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Mathematical Sciences: Boundary Layer Phenomena for Functional Differential Equations and Means and Their Iterations

数学科学：泛函微分方程和均值及其迭代的边界层现象

基本信息

批准号：
8903018
负责人：
Roger Nussbaum
金额：
$ 5.56万
依托单位：
Rutgers University New Brunswick
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：
1989-07-15 至 1991-12-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=8903018&HistoricalAwards=false
关键词：
Mathematical Sciences Boundary Layer Phenomena

项目摘要

This project continues work on the mathematical theory of functional differential equations. Of particular interest are those equations involving time delay and the presence of a negative feed-back condition. Singular perturbation methods will be employed. Equations of this type arise in a number of applications such as optics, physiology and mathematical biology. Considerable progress has been made on these equations. Emphasis will be placed on understanding the dynamics of solutions having prescribed values given over an interval. A particular instance would be to give conditions for the existence of slowly varying solutions. Other work will focus on equations where one has state dependent time lags which model blood cell production and agricultural commodity cycles. Here again, one looks for periodicity properties of solutions as well as insight into the asymptotic properties of solutions as the perturbation parameter tends to zero. Another class of problems to be considered involves functional differential equations where the forcing functional depends on the delayed values of the solution as well as the current values. Here the primary object is to determine if there are no nonconstant solutions of period equal to four. Examples indicate that this conjecture is true, although its validity is by no means assured.

这个项目继续研究泛函微分方程的数学理论。特别令人感兴趣的是那些涉及时间延迟和存在负反馈条件的方程。将采用奇异摄动方法。这种类型的方程出现在光学、生理学和数学生物学等许多应用中。在这些方程式上已经取得了相当大的进展。重点将放在理解在一段时间内给定给定值的解的动力学上。一个特殊的例子是给出慢变解存在的条件。其他工作将集中在具有状态依赖时间滞后的方程上，这些方程模拟血细胞生产和农业商品周期。在这里，我们寻找解的周期性性质以及当扰动参数趋于零时解的渐近性质。要考虑的另一类问题涉及泛函微分方程，其中强迫泛函取决于解的延迟值以及当前值。这里的主要目的是确定是否不存在周期为4的非常解。实例表明，这一猜想是正确的，尽管它的有效性绝不能得到保证。