Visiting Karlsruhe for a couple of days, and giving a presentation in the Nonlinear Partial Differential Equations seminar.

Title: Orbital stability for monostable fronts in reaction-diffusion equations

Abstract: In this presentation, I will discuss the long-time asymptotic stability of a particular class of travelling waves. Monostable fronts are heteroclinic connections between linearly stable and linearly unstable constant equilibria. Until now, all known stability result assume additional localization of the initial perturbation. We will see how to remove this condition to show orbital stability with respect to phase shift.