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

Texas A&M Research Foundation, College Station TX

Investigators

Abstract

Stability of Shock Waves and Related Structures in Combustion Models, Thin Film Flows and General Conservative Systems. Abstract of proposed research Peter B Howard Under 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.