Hyperbolic Systems of Conservation Laws and Applications

守恒定律的双曲系统及其应用

基本信息

  • 批准号:
    0803463
  • 负责人:
  • 金额:
    $ 5.98万
  • 依托单位:
  • 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:
    2007-08-31 至 2010-06-30
  • 项目状态:
    已结题

项目摘要

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.
这项研究计划涉及守恒律的双曲型系统理论的几个方面,并涉及可分为两类的项目。第一类是将零粘性方法应用于(A)具有弱耗散机制的双曲型方程组(如摩擦、衰减记忆和松弛)和(B)具有大初始数据的特殊双曲型守恒律组。这些项目将建立具有重要应用的系统解的存在性、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。第二类是双曲型守恒律组的熵弱解对物理参数的连续依赖性,如绝热指数和光速。这些项目的目的是启动对非线性通量函数的依赖问题的研究,并将其应用于气体动力学和特殊相对论中的可压缩流体。本研究项目涉及连续介质物理和双曲型守恒定律理论之间的接口问题。在弹性、塑性、流体力学、半导体、气体动力学和燃烧研究中出现的大多数偏微分方程式都可以表述为守恒定律。这个项目研究这种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统物理。该计划的结果也有望提出将推进系统数值模拟的计算算法。

项目成果

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Cleopatra Christoforou其他文献

A discrete variational scheme for isentropic processes in polyconvex thermoelasticity
On the decay rate of the Gauss curvature for isometric immersions

Cleopatra Christoforou的其他文献

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{{ truncateString('Cleopatra Christoforou', 18)}}的其他基金

Hyperbolic Systems of Conservation Laws and Applications
守恒定律的双曲系统及其应用
  • 批准号:
    0708137
  • 财政年份:
    2007
  • 资助金额:
    $ 5.98万
  • 项目类别:
    Standard Grant

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双曲守恒定律系统的稳定性理论
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