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

这是一个研究非线性部分 奇异微分方程 扰动，最优控制理论和微分对策， 力学、非线性波等。本课程的一般主题 研究包括： a）反应扩散型奇异摄动; B）第一- 以及Hamilton-Jacobi-Bellman-Isaacs类型的二阶偏微分方程; c）多孔介质方程; d）非线性波。 这些主题由以下共同方法统一起来： 偏微分方程 本研究是应用数学分析的一部分。

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.