Evolutionary Systems and Weighted Translation Operators

进化系统和加权翻译算子

• 批准号: 9400518
• 负责人: Yuri Latushkin
• 金额: $ 4.12万
• 依托单位: University of Missouri-Columbia
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9400518&HistoricalAwards=false
• 关键词: Evolutionary; Systems; Weighted; Translation; Operators

9400518 Latushkin The Principal Investigator proposes to solve some problems at the intersection of the asymptotic theory of linear semigroups and infinite dimensional dynamical systems to describe the asymptotic properties (dichotomy, hyberbolicity, Lyapunov exponents) of evolutionary systems and semiflows on Banach spaces. The main technical tool is to involve for this description the semigroups of weighted translation operators. This technique would allow one to view the classical Lyapunov theorems in a fairly unexpected perspective. This work has its roots in the analysis of stability of processes. These processes are frequently described by differential equations and the stability is determined by an analysis of the asymptotic or large time behavior of the solutions. The solutions of these equations live naturally in abstract structures called Banach spaces and the study of stability questions can be formulated in terms of a metric or norm. In this way the techniques of operator theory can be used effectively to study stability of dynamical systems. The theory has applications in dynamo theory and the dynamics of chemical reactors. ***

9400518 Latushkin 首席研究员提出解决线性半群渐近理论和无限维动力系统相交的一些问题，以描述演化系统和巴拿赫空间上的半流的渐近性质（二分法、双曲性、Lyapunov 指数）。主要的技术工具是涉及加权翻译算子半群的描述。这种技术可以让人们以一种相当意想不到的视角来看待经典的李亚普诺夫定理。 这项工作源于过程稳定性分析。这些过程经常用微分方程描述，稳定性是通过对解的渐近或大时间行为的分析来确定的。这些方程的解自然地存在于称为巴纳赫空间的抽象结构中，稳定性问题的研究可以用度量或范数来表述。这样算子理论的技术可以有效地用于研究动力系统的稳定性。 该理论在发电机理论和化学反应器动力学中具有应用。 ***