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主要研究者提议在线性半群和无限尺寸动力学系统的渐近理论上解决一些问题，以描述进化系统和班ach频道上的渐近性特性（二分法，氢化植物，Lyapunov指数）。主要的技术工具是参与此描述的加权翻译操作员的半群。该技术将使人们可以从相当出乎意料的角度查看经典的Lyapunov定理。 这项工作源于过程的稳定性。这些过程经常通过微分方程来描述，稳定性是通过对解决方案的渐近或大时间行为的分析来确定的。这些方程式的解决方案自然生活在称为Banach空间的抽象结构中，并且可以根据度量或规范来提出稳定问题的研究。通过这种方式，可以有效地使用运算符理论的技术来研究动力系统的稳定性。 该理论在发电机理论和化学反应堆的动力学中有应用。 ***