Differential Equations Seminar

Title: Wavespeed selection in systems of reaction-diffusion equations

Abstract: Wavespeed selection refers to the problem of determining the long time asymptotic speed of invasion of an unstable homogeneous state by some other secondary state. This talk will review wavespeed selection mechanisms in the context of reaction-diffusion equations. Particular emphasis will be placed on the qualitative differences between wavespeed selection in systems of reaction-diffusion equations and scalar problems as well as some surprising consequences. We 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 and some examples of coupled Fisher-KPP equations.