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.

首席研究员和他的合作者研究双曲守恒律，一类偏微分方程，涵盖了应用数学中的许多基本方程，特别是流体动力学。目前研究的主要思路是：（A）基于特征标架的几何性质，系统地研究一维守恒律方程组：（B）利用消失粘性近似，得到多维守恒律方程组的相互作用估计;（C）守恒律系统的径向对称解，特别是可压缩欧拉系统的解。所有这些项目的动机都是为了提供科学家和工程师所使用的物理模型的性质的严格声明。结果评估各种物理模型的有效性范围，并将用于界定和完善现有的模型。特别强调的是理解复杂的非线性方程的解，这些方程用于模拟例如高速飞行，交通流量，燃烧和爆炸。