Shock waves and reaction-diffusion equations (Grundlehren der mathematischen Wissenschaften)

The purpose of this book is to make easily available the basics of the theory of hyperbolic conservation laws and the theory of systems of reaction-diffusion equations, including the generalized Morse theory as developed by Charles Conley. It presents the modern ideas in these fields in a way that is accessible to a wider audience than just mathematicians. The book is divided into four main parts: linear theory, reaction-diffusion equations, shock-wave theory, and the Conley index. For the second edition, typographical errors and other mistakes have been corrected and a new chapter on recent results has been added. The new chapter contains discussion of the stability of travelling waves, symmetry-breaking bifurcations, compensated compactness, viscous profiles for shock waves, and general notions for constructing travelling-wave solutions for systems of non-linear equations.