Mathematical Sciences: Theory and Applications of Functionaland Partial Differential Equations

数学科学：泛函和偏微分方程的理论与应用

基本信息

批准号：
9208818
负责人：
Kenneth Cooke
金额：
$ 5.08万
依托单位：
Pomona College
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
1992
资助国家：
美国
起止时间：
1992-08-15 至 1995-01-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=9208818&HistoricalAwards=false
关键词：
Mathematical Sciences Theory Applications Functionaland

项目摘要

This project continues research on theoretical and applied problems involving functional and partial differential equations. Work will be done investigating the stability and Hopf bifurcation problems for a general class of functional differential equations with state-dependent bounded delay. Another line of study concerns singularly perturbed nonlinear differential difference equations where the goal is to show the existence of a pulse-like periodic solutions. Several problems involving the existence of distributional solutions of classes of partial differential equations. Closer to immediate applications, work will be done on the dynamics of population models. It includes a generalization of Volterra's population equation to include spatially distributed population and delay in the birth process. Models for disease transmission of sexually transmitted diseases will also be analyzed. Here the additional element in the model incorporates risk-behavior change. Differential equations form the backbone of mathematical modeling in the biological sciences. Phenomena which involve continuous change such as that seen in motion, materials and energy are known to obey certain general laws which are expressible in terms of the interactions and relationships between partial derivatives. The key role of mathematics is not only to state the relationships, but also to extract qualitative and quantitative meaning from them.

该项目继续研究涉及功能和部分微分方程的理论和应用问题。将完成研究一类具有状态依赖性限制延迟的一类功能分化方程的稳定性和HOPF分叉问题。另一项研究涉及单一扰动的非线性差异差方程，其中的目标是显示出类似脉冲的周期溶液的存在。涉及偏微分方程类别的分布解决方案存在的几个问题。更接近即时应用，将对人口模型的动态进行工作。它包括对Volterra种群方程式的概括，包括空间分布的人群和延迟出生过程。还将分析用于性传播疾病的疾病传播模型。在这里，模型中的附加元素包含风险行为变化。微分方程构成了生物科学中数学建模的骨干。涉及持续变化的现象，例如在运动，材料和能量中看到的现象，以遵守某些从部分衍生物之间的相互作用和关系来表达的一般定律。数学的关键作用不仅是陈述关系，而且是从它们中提取定性和定量含义。