Hyperbolic Systems of Conservation Laws and Applications

守恒定律的双曲系统及其应用

• 批准号: 0708137
• 负责人: Cleopatra Christoforou
• 金额: $ 8.01万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-07-01 至 2008-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0708137&HistoricalAwards=false
• 关键词: Hyperbolic; Systems; Conservation; Laws; Applications

This research program deals with several aspects of the theory of hyperbolic systems of conservation laws and involves projects that can be divided into two categories. The first category is the application of the method of vanishing viscosity to (a) hyperbolic systems with weakly dissipative mechanisms such as friction, fading memory, and relaxation and (b) special systems of hyperbolic conservation laws with large initial data. These projects will establish the existence, stability, and qualitative behavior of solutions to systems with important applications; for example, porous media flows and the motion of viscoelastic materials with fading memory. The second category is the continuous dependence of entropy weak solutions to hyperbolic systems of conservation laws on physical parameters such as the adiabatic exponent and speed of light. The aim of these projects is to initiate an investigation on this issue of dependence on nonlinear flux functions with applications to compressible fluids in gas dynamics and special relativity.This research project concerns problems lying on the interface between continuum physics and the theory of hyperbolic systems of conservation laws. Most of the partial differential equations arising in the study of elasticity, plasticity, fluid mechanics, semiconductors, gas dynamics, and combustion can be formulated as conservation laws. This project investigates mathematical properties of systems of such conservation laws, making use of the underlying physical structure to direct the analysis, while conversely elucidating properties of the equations to help better understand continuum physics. The results of this program are also expected to suggest computational algorithms that will advance numerical simulation of the systems.

这个研究计划涉及守恒律双曲系统理论的几个方面，涉及的项目可以分为两类。 第一类是应用的方法消失粘度（a）双曲系统与弱耗散机制，如摩擦，褪色记忆，和松弛和（B）特殊系统的双曲守恒律与大的初始数据。 这些项目将建立具有重要应用的系统解决方案的存在性，稳定性和定性行为;例如，多孔介质流动和具有衰减记忆的粘弹性材料的运动。 第二类是双曲守恒律方程组的熵弱解对绝热指数和光速等物理参数的连续依赖性。 这些项目的目的是开始研究这个问题的依赖于非线性通量函数与应用于可压缩流体在气体动力学和狭义相对论。这个研究项目涉及的问题之间的接口连续物理和双曲守恒定律系统的理论。 在弹性、塑性、流体力学、半导体、气体动力学和燃烧的研究中产生的大多数偏微分方程都可以用守恒定律来表述。 该项目研究此类守恒定律系统的数学性质，利用基本的物理结构来指导分析，同时反过来阐明方程的性质，以帮助更好地理解连续介质物理学。 该计划的结果也有望提出计算算法，将推进系统的数值模拟。