Mathematical Sciences: Theory and Application of Linear Ordinary Differential Equations

数学科学：线性常微分方程的理论与应用

• 批准号: 9001483
• 负责人: Russell Johnson
• 金额: $ 10.24万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-01 至 1992-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001483&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Theory; Application; Linear

Professor Johnson will study linear differential operators with bounded but non-decaying coefficients (which might be almost periodic or paths of an ergodic process). Using techniques from dynamical systems theory, he will study spectral properties and generalized Floquet exponents for such operators. He will apply his results in the following areas: bifurcation from invariant tori in non-linear dynamical systems; spectral properties of the one-dimensional almost periodic Schroedinger operator; linear optimal control theory; the topological index theory of non- periodic ordinary and partial differential equations, and its relation with cohomology theory of certain C* algebras; the Korteweg-deVries equation with bounded initial data. Johnson's research in differential equations is very broadly based and has implications for a variety of fields ranging from pure mathematics to physics and engineering.

约翰逊教授将研究具有有界但非衰减系数的线性微分算子（可能几乎是周期性的或遍历过程的路径）。 他将利用动力系统理论的技术，研究此类算子的谱特性和广义 Floquet 指数。 他将把他的成果应用到以下领域：非线性动力系统中不变环面的分岔；一维几乎周期性薛定谔算子的光谱特性；线性最优控制理论；非周期常微分方程和偏微分方程的拓扑指数理论及其与某些C*代数的上同调理论的关系；具有有界初始数据的 Korteweg-deVries 方程。 约翰逊在微分方程方面的研究基础非常广泛，对从纯数学到物理和工程学的各个领域都有影响。