Presenting at the MUSCA team seminar.

Title: Existence and stability of invasion fronts.

Abstract: Invasion fronts are travelling waves that approach a linearly unstable equilibrium state. They often appear in biology, for example when an alien species invades an empty territory. In this presentation, we will review recent results about existence and long time stability of these solutions. We will see that use of exponential weights is necessary in two different contexts: For a space-continuous hyperbolic equation and for a space-discretized parabolic equation. These are joint works with L. M. rodrigues and H. J. Hupkes.