Mathematical Sciences: Research in Dynamic Problems Arising in Mechanics and Control

数学科学：力学和控制中出现的动态问题的研究

• 批准号: 9006945
• 负责人: Marshall Slemrod
• 金额: $ 18万
• 依托单位: University of Wisconsin-Madison
• 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: 1991-03-01 至 1994-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9006945&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Dynamic; Problems

The principal investigator will continue his research on several topics in the dynamics of continua. In particular, he will study continuum and kinetic theories of material motion undergoing phase transitions, initial value problems for the Riemann problem for systems of hyperbolic conservation laws, and distributed-parameter control systems. The tools used will be various techniques from the qualitative theory of partial differential equations and from nonlinear analysis. Many natural phenomena involve the transition of a material from one phase to another. As an example, think of what happens to the ice cubes in your drink. The principal investigator will apply modern methods of nonlinear analysis to study the dynamical behavior of materials undergoing phase transitions and also ways to control the instabilities that often result when materials are stressed.

首席研究员将继续他对连续介质动力学中的几个主题的研究。特别是，他将研究经历相变的物质运动的连续体和动力学理论，双曲型守恒律组的黎曼问题的初值问题，以及分布参数控制系统。所使用的工具将是来自偏微分方程组定性理论和非线性分析的各种技术。许多自然现象都涉及到物质从一种相到另一种相的转变。举个例子，想想你饮料里的冰块发生了什么事。主要的研究人员将应用现代非线性分析方法来研究经历相变的材料的动力学行为，以及控制材料在受力时经常产生的不稳定性的方法。