Mathematical Sciences: Shock Stability in Systems that Change Type

数学科学：改变类型的系统的冲击稳定性

• 批准号: 9103560
• 负责人: Barbara Keyfitz
• 金额: $ 0.5万
• 依托单位: University of Houston
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1993-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9103560&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Shock; Stability; Systems

In this project the principal investigator will continue her important work on the well-posedness of systems of partial differential equations that can change type. Such systems have solutions of shock-wave type that serve as mechanisms for the propoagation of waves, even in parts of the domain where the system is no longer hyperbolic. These types of problems occur in the transonic flow of gases and in the flow of multi-phase fluids through porous media. In particular, the principal investigator will study the stability of shock waves in systems of equations that undergo changes from hyperbolic to elliptic type using regularization and perturbation methods. The behavior of fluids (liquids and gases) under unusual conditions such as in the upper atmosphere or in the earth is governed by a complicated system of partial differential equations that can under go what is called a "change of type". Basically this means that the system has solutions of different kinds in different parts of the domain. As an illustration, think of the behavior of a seismic wave generated inside the earth by a earthquake. The wave passes through regions that are in liquid, solid or composite states. In this project the principal investigator will examine certain solutions of a system of model equations that exhibit change-of-type behavior that are known as "shock waves". The study of shock waves arises in such technologically important areas as transonic flow and flow through porous media.

在这个项目中，主要研究人员将继续她在可以改变类型的部分微分方程系统的良好系统方面的重要工作。 这样的系统具有冲击波类型的解决方案，即使在系统不再是双曲线的域的某些部分，也可以用作波的预防。 这些类型的问题出现在气体的跨气流以及多孔介质的多相流体流中。 特别是，主要研究者将使用正则化和扰动方法研究在从双曲线到椭圆类型的方程式系统中进行冲击波的稳定性。 在异常条件下，例如在高层大气或地球中的流体（液体和气体）的行为，受部分微分方程的复杂系统的控制，这些系统可以在所谓的“类型变化”下进行。 基本上，这意味着系统在域的不同部分具有不同种类的解决方案。 作为例证，想到地震在地球内产生的地震波的行为。 波穿过液体，固体或复合态的区域。 在该项目中，主要研究者将检查模型方程系统的某些解决方案，该系统表现出称为“冲击波”的式行为。 冲击波的研究是在技术上重要的领域中出现的，例如跨气流和流过多孔介质的流动。