Shock Waves and Reaction-Diffusion Equations

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.