Small Viscosity and Boundary Layer Methods

This book has evolved from lectures and graduate courses given in Brescia (Italy), Bordeaux and Toulouse (France};' It is intended to serve as an intro­ duction to the stability analysis of noncharacteristic multidimensional small viscosity boundary layers developed in (MZl]. This book is an introduction to the stability analysis of noncharacteristic boundary layers, emphasizing selected topics and developing mathematical tools relevant to the study of multidimensional problems. Boundary layers are present in problems from physics, engineering, mechanics, and fluid mechanics and typically appear for problems with small diffusion. Boundary layers also occur in free boundary value problems, particularly in the analysis of shock waves. The main goal of this presentation is to provide basic tools for the understanding of multidimensional boundary layers for systems. Included are self-contained introductions to different topics such as hyperbolic boundary value problems, parabolic systems, WKB methods, construction of profiles, introduction to the theory of Evans? functions, and energy methods with Kreiss? symmetrizers.