Mathematical Sciences: Research on Nonlinear Partial Differential Equations with Applications to Singular Perturbations, Optimal Control and Differential Games

数学科学：非线性偏微分方程研究及其在奇异扰动、最优控制和微分博弈中的应用

• 批准号: 8801208
• 负责人: Panagiotis Souganidis
• 金额: $ 10.17万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-15 至 1991-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8801208&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Nonlinear; Partial

This is a project for research on nonlinear partial differential equations with applications to singular perturbations, optimal control theory and differential games, mechanics, nonlinear waves, etc. The general topics of this research include: a) Singular perturbations of reaction-diffusion type; b) First- and second-order PDE's of Hamilton-Jacobi-Bellman-Isaacs type; c) Porous medium equations; d) Nonlinear waves. These topics are unified by the common methodology of partial differential equations. This research is part of applied mathematical analysis.

这是一个研究非线性偏微分方程及其在奇异摄动、最优控制理论和微分对策、力学、非线性波等方面应用的项目。本研究的一般主题包括：a)反应扩散型奇异摄动；b) Hamilton-Jacobi-Bellman-Isaacs型一阶和二阶偏微分方程；c)多孔介质方程；d)非线性波。这些主题由偏微分方程的通用方法统一起来。本研究是应用数学分析的一部分。