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.

该项目继续对功能微分方程的数学理论进行工作。特别令人感兴趣的是涉及时间延迟的方程式和负反喂养条件的情况。将采用单数扰动方法。这种类型的方程在许多应用中出现，例如光学，生理和数学生物学。这些方程式已经取得了很大进展。重点将放在理解在间隔内给出的规定值的解决方案的动力学。一个特定的实例是给出存在缓慢变化的解决方案的条件。其他工作将集中在一个方程式上，其中一个具有状态依赖的时间滞后，这些时间滞后对血细胞的产生和农产品周期进行了建模。在这里，人们再次寻找解决方案的周期性特性，以及对溶液的渐近特性的洞察力，因为扰动参数往往为零。要考虑的另一类问题涉及功能分化方程，其中强迫功能取决于解决方案的延迟值以及当前值。这里的主要对象是确定是否没有等于四的周期解决方案。例子表明，尽管没有确保其有效性，但该猜想是正确的。