Mathematical Sciences: Large Scale Oscillatory Behavior Arising from Nonlinear Systems

数学科学：非线性系统引起的大规模振荡行为

• 批准号: 9102330
• 负责人: Alan Lazer
• 金额: $ 12.04万
• 依托单位: University of Miami
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-01 至 1994-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9102330&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Large; Scale; Oscillatory

This research involves the following principle: imposing large loading on asymmetric systems results in highly oscillatory behavior. The greater the asymmetry, the larger the number of oscillatory solutions. This research applies this principle in one form or another to nonlinear boundary value problems of elliptic, hyperbolic, and parabolic type as well as with ordinary differential equations and Hamiltonian systems. In the periodic case, there is a considerable body of information which suggests that some of these solutions are asymptotically stable and commonly occurring. This work has led to new insights into nonlinear periodic oscillations in suspended masses, rods and beams, and in floating beams. This research is in the general area of applied mathematics. The project involves a mixture of analytic theory, functional analysis, numerical and computational analysis, and an extension of these results to concrete engineering problems such as the structure of bridges and ships.

本研究涉及以下原则： 非对称系统上的负载导致高度振荡行为。 不对称性越大，振荡的数量就越大 解决方案 这项研究以这样或那样的形式应用了这一原则 椭圆型、双曲型和 抛物型以及常微分方程， 汉密尔顿系统。 在周期性的情况下， 这些信息表明，其中一些解决方案是 渐近稳定且通常发生。 这项工作导致了新的 对悬挂质量、杆、 梁和浮动梁。 这项研究是在应用数学的一般领域。 的 项目涉及分析理论，功能分析， 数值和计算分析，以及这些结果的扩展 具体的工程问题，如桥梁结构， 船舶