Laboratoire de Physique Théorique
Toulouse - UMR 5152

A moving interface, or a front, between a stable and an unstable medium is often described by an equation such as the Fisher-KPP equation :

∂u ∂²u —— = ——— + u - u² ∂t ∂x²

Such an equation appears in biology, chemistry or theoretical physics. Thirty years ago, Bramson gave rigorous sharp estimates on the position of the front, and, fifteen years ago, Ebert and van Saarloos heuristically identified universal vanishing corrections.

In this seminar, I will present two new front equations which we believe to be in the same universality class as the Fisher-KPP equation. For the first equation, we can write an exact relation between the initial condition and the positions of the front at all times. For the second equation, probabilistic methods give very good estimates on the shape of the front at all times. In both cases, we can recover and make precise the universal vanishing corrections on the position of the front.