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.

本项目继续进行理论和应用研究， 涉及泛函和偏微分方程的问题。 工作将做调查的稳定性和霍普夫 一类泛函的分歧问题 状态依赖有界时滞微分方程 另一个研究方向是奇异摄动非线性 微分差分方程的目标是显示 脉冲型周期解的存在性 几个问题 涉及到的类的分布解的存在性 偏微分方程 更接近即时 应用程序，将在人口动态方面开展工作 模型 它包括了对沃尔泰拉人口的概括 方程，包括空间分布的人口和延迟 出生过程。 性传播疾病模型 还将分析传染病。 在这里， 模型中的元素包含风险行为变化。 微分方程是数学的主干 生物科学中的建模。 现象涉及 连续变化，如在运动中看到的，材料和 已知能量服从某些一般定律， 可以用相互作用和关系来表达 偏导数之间的关系 数学的关键作用不是 不仅要陈述关系，还要提取定性的 和量化的意义。