Patterns and Waves

This textbook is concerned with the study of certain classes of nonlinear partial differential equations known collectively as reaction-diffusion equations. It aims to provide an introduction to the theory of these equations, to give a compendium of useful techniques for their analysis, and to show how these techniques find application in a variety of settings, notably in pattern formation and non-planar wave-like structures. Throughout, there are fully worked examples to illustrate the salient themes of the discussions. Readers are expected to have a firm background in the theory of differential equations, and the basis of functional analysis.