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

• 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

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泛函和偏微分方程的理论和应用问题。 我们将研究一类具有状态相关有界时滞的函数微分方程的稳定性和 Hopf 分岔问题。 另一项研究涉及奇异扰动非线性微分方程，其目标是证明类脉冲周期解的存在。 涉及偏微分方程类分布解的存在性的几个问题。 更接近直接应用，将开展人口模型动态方面的工作。 它包括沃尔泰拉人口方程的推广，包括空间分布的人口和出生过程的延迟。 还将分析性传播疾病的传播模型。 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支柱。 涉及连续变化的现象，例如在运动、材料和能量中看到的现象，已知遵守某些一般定律，这些定律可以用偏导数之间的相互作用和关系来表达。 数学的关键作用不仅是陈述关系，而且还从中提取定性和定量的意义。