Shock Waves and Reaction-Diffusion Equations
by Joel Smoller
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 numerous typographical
errors and other mistakes have been corrected and a new chapter on recent results
has been added. The new chapter contains discussions of the stability of traveling
waves, symmetry-breaking bifurcations, compensated compactness, viscous profiles
for shock waves, and general notions for construction traveling-wave solutions
for systems of nonlinear equations.
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The above is from the Springer website.