Reaction-Diffusion Equations in Homogeneous Media: Existence, Uniqueness and Stability of Travelling Fronts

The goal of this survey is to describe the construction and some qualitative properties of particular global solutions of certain reaction-diffusion equations. These solutions are known as travelling fronts (or travelling waves) and play an important role in the long-time behaviour of the solutions of the parabolic system. We will mainly focus on the existence of travelling wave solutions and their stability. We will also give some standard tools in elliptic and parabolic theory, which are of general interest.