US-Federal Republic of Germany Cooperative Research: Almost Periodicity and Asymptotics for Semigroups of Operators

美德合作研究：算子半群的近似周期性和渐近性

• 批准号: 8822565
• 负责人: W. Summers
• 金额: $ 1.02万
• 依托单位: University of Arkansas
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-07-01 至 1993-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8822565&HistoricalAwards=false
• 关键词: US; Federal; Republic; Germany; Cooperative

This award supports Professor W. H. Summers of the University of Arkansas to collaborate in research with Professor Wolfgang M. Ruess of the Mathematics Department, University of Essen, West Germany. In previous joint work, these investigators have combined complementary backgrounds to develop criteria and techniques which have proved useful in resolving some longstanding problems by providing new insight into dynamical phenomena that are asymptotically close to being almost periodic. The proposed cooperative research program will continue this line of investigation. The goal of the research is to identify conditions on the semigroup, its generator, and the initial values under which trajectories are asymptotically almost periodic in some appropriate sense. Both the expected and existing results in this direction will be applied to questions concerning the existence and description of strong or weak limits of ergodic means, asymptotic behavior of solutions to the Cauchy problem and functional differential equations with infinite delay, and asymptotic behavior of age-dependent population models. Mathematical models for many time-dependent processes in physics, chemistry and biology take the form of a Cauchy problem associated with the generator of a semigroup of operators on an appropriate Banach state space. The future-time behavior of the process can then be investigated by studying asymptotic properties of motions and almost-orbits of the corresponding semigroup. There has been considerable effort devoted by many researchers in recent years to classifying the asymptotic behavior of nonlinear semigroups. A great variety of results has been established by different methods. Drs. Summers and Ruess have brought new techniques and insights to the problem, and have recently produced some very interesting contributions to this subject. They are now beginning to seek new applications of their results, in particular to nonlinear functional differential equations.

该奖项支持W教授。H.大学的夏天 阿肯色州与沃尔夫冈M. 西埃森大学数学系的Ruess 德国。 在以前的联合工作中，这些调查人员联合了 互补的背景，以制定标准和技术， 在解决一些长期存在的问题方面证明是有用的， 提供了对动力学现象的新见解， 渐近地接近于几乎周期性。 拟议 合作研究计划将继续这一路线， 调查 这项研究的目的是确定 关于半群，它的生成元，以及在其下的初始值， 轨迹是渐近几乎周期在一些适当的 道理啊 这方面的预期成果和现有成果 将适用于有关存在的问题， 遍历平均的强极限或弱极限的渐近描述 柯西问题和泛函解的行为 无穷时滞微分方程的渐近性态 年龄相关的人口模型。 物理学中许多与时间有关的过程的数学模型， 化学和生物学都是柯西问题， 一个适当的算子半群的生成元 Banach状态空间 进程的未来行为可以 然后通过研究运动的渐近性质 以及相应半群的几乎轨道。 出现 近年来，许多研究人员投入了大量精力， 分类非线性半群的渐近行为。 一 各种各样的结果已经建立了不同的 方法. 萨默斯和鲁斯博士带来了新的技术， 对这个问题的见解，最近产生了一些非常 对这个主题的有趣贡献。 他们现在开始 寻求其成果的新应用，特别是 非线性泛函微分方程