Mathematical Sciences: Traveling Wave Solutions of Reaction Diffusion Systems

数学科学：反应扩散系统的行波解

• 批准号: 8702693
• 负责人: David Terman
• 金额: $ 5.67万
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-06-01 至 1990-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8702693&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Traveling; Wave; Solutions

Reaction-diffusion equations arise as models in many areas of Mathematical Biology and Chemistry. A feature common to many of these systems is the existence of traveling wave solutions. These correspond to solutions which appear to be traveling with constant shape and velocity. The objective of this project is to develop new techniques for proving the existence and stability of traveling wave solutions. There are two basic steps in the program outlined in this project. The first consists of developing general methods for proving the existence and stability of traveling wave solutions. A basic ingredient for these methods is the Conley index, a relatively recent tool developed by the late Professor Charles Conley in 1977-1978. The second part consists of applications of the basic theory. Specific applications to be considered are the existence and stability of traveling wave solutions arising from ecology and combustion, and the existence of radially symmetric solutions of semilinear elliptic systems. This last problem is closely related to the question of the existence of traveling wave solutions. The project presented by Professor Terman contains several sub- projects related to various potential connections of this mathematical theory to other scientific problems. Professor Terman is a young talented mathematician who has already established his leading position in this area of research.

反应扩散方程作为模型出现在数学生物学和化学的许多领域。 许多这些系统的共同特征是行波解的存在。 这些对应于似乎以恒定形状和速度行进的解。 该项目的目标是开发新技术来证明行波解的存在性和稳定性。 该项目概述的程序有两个基本步骤。第一个包括开发证明行波解的存在性和稳定性的通用方法。 这些方法的基本要素是康利指数，这是已故查尔斯·康利教授于 1977 年至 1978 年开发的一种相对较新的工具。 第二部分是基础理论的应用。 要考虑的具体应用是生态和燃烧产生的行波解的存在性和稳定性，以及半线性椭圆系统径向对称解的存在性。 最后一个问题与行波解的存在性问题密切相关。 特曼教授提出的项目包含几个与该数学理论与其他科学问题的各种潜在联系相关的子项目。 Terman教授是一位年轻的天才数学家，他已经在该研究领域确立了自己的领先地位。