Stability of Shock Waves and Related Structures in Combustion Models, Thin Film Flows, and General Conservative Systems

燃烧模型、薄膜流和一般保守系统中冲击波和相关结构的稳定性。拟议研究摘要Peter B Howard根据该奖项，将研究正则化和部分正则化守恒律背景下产生的非线性波的稳定性。特别是，我们将调查的稳定性退化的粘性冲击波，如燃烧模型中出现的，稳定的压缩和欠压缩的粘性冲击波中出现的薄膜流动模型，更一般地说，压缩，过-和欠压缩的粘性冲击波中出现的系统，如可压缩的Navier-Stokes方程，只有部分正则化。 我们还将研究相关系统中稀疏波的稳定性，以及燃烧理论中出现的稀疏-压缩模式的稳定性，以及薄膜流动研究中出现的欠压缩-压缩模式。 所使用的方法涉及应用绿色的功能和埃文斯function.The更广泛的影响，这项研究在于深入了解我们的模型和物理过程，他们的基础上。 通过研究的稳定性，我们的系统的基本方面的特点，可以出现的物理观察到的现象和解决方案的长期行为的类型。 我们还获得了关键的洞察力，我们的模型捕捉它们所代表的底层物理的准确性。 此外，所开发的技术应在一系列相关系统的分析中得到应用。

Stability of Shock Waves and Related Structures in Combustion Models,Thin Film Flows and General Conservative Systems.Abstract of proposed researchPeter B HowardUnder this award the stability of nonlinear waves arising in the context of regularized and partially regularized conservation laws will be studied. In particular we shall investigate the stability of degenerate viscous shock waves such as arise in combustion models, the stability of compressive and undercompressive viscous shock waves that arise in models of thin film flows, and more generally, compressive, over- and undercompressive viscous shock waves that arise in systems such as the compressible Navier--Stokes equations with only partial regularization. We shall also investigate the stability of rarefaction waves in related systems, and the stability of rarefaction-compressive patterns that arise in combustion theory as well as the undercompressive-compressive patterns that arise in the study of thin film flows. The methods to be used involve the application of Green's functions and the Evans function.The broader impact of this research lies in the insight gained into our models and the physical processes on which they are based. Through a study of stability, we characterize such fundamental aspects of our systems as the types of physically observable phenomena that can arise and the long time behavior of solutions. We also gain critical insight into the accuracy with which our models capture the underlying physics they represent. In addition, the techniques developed should find application in the analysis of a range of related systems.