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Abstract

Wavespeed selection refers to the problem of determining the long time asymptotic speed of invasion of an unstable state by some secondary state. This tutorial will discuss wavespeed selection mechanisms for reaction-diffusion equations. Particular emphasis will be placed on the qualitative differences between wavespeed selection in systems of reaction diffusion equations and scalar problems. The tutorial will review the notions of the linear spreading speed, pushed and pulled fronts, marginal stability and the role of singularities of the pointwise Green's function. Examples will include a Lotka-Volterra competition model, the Keller-Segel model, and some examples of coupled Fisher-KPP equations.