Entropies, geometric structures, and interactions for systems of conservation laws

守恒定律系统的熵、几何结构和相互作用

• 批准号: 1009002
• 负责人: Helge Jenssen
• 金额: $ 14.03万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-07-01 至 2013-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1009002&HistoricalAwards=false
• 关键词: Entropies; geometric; structures; interactions; systems

The Principal Investigator and his collaborators study hyperbolic conservation laws, a class of partial differential equations that covers many of the fundamental equations in applied math, and in particular in fluid dynamics. The main lines of current research are: (A) a systematic approach to the study of one-dimensional systems of conservation laws based on geometric properties of their eigen-frames; (B) employing vanishing viscosity approximations to obtain interaction estimates for conservation laws in several space dimensions; (C) radially symmetric solutions to systems of conservation laws, and in particular solutions to the compressible Euler system.All of the projects are motivated by the need to provide rigorous statements about the properties of physical models that are used by scientists and engineers. The results assess the range of validity of various physical models and will be of use in delimiting and refining existing models. Particular emphasis is put on understanding solutions of complex, nonlinear equations that are used in simulations of e.g. high speed flight, traffic flow, combustion and detonations.

首席研究员及其合作者研究双曲线保护法，这是一类部分微分方程，涵盖了应用数学的许多基本方程，尤其是流体动力学。当前研究的主要线路是：（a）一种基于其本征框架的几何特性研究一维保护定律的系统方法； （b）采用消失的粘度近似来获得几个空间维度的保护定律的相互作用估计； （c）对保护法系统的径向对称解决方案，尤其是针对可压缩的Euler系统的解决方案。所有项目的动机都是由于需要提供有关科学家和工程师使用的物理模型特性的严格陈述。结果评估了各种物理模型的有效性范围，并将用于划定和完善现有模型。特别强调的是理解在模拟中使用的复杂，非线性方程的解决方案。高速飞行，交通流量，燃烧和爆炸。