Travelling waves for the random KPP equation

Joseph Conlon university of michigan, USA

This talk will present recent results of Charles Doering and the speaker on properties of the wave speed for the stochastically perturbed KPP equation. It was shown in the classical 1937 paper by Kolmogorov, Petrowskii and Piscunov that the large time behavior of the solution to the KPP equation with Heaviside initial data is a travelling wave. In a seminal 1995 paper Mueller and Sowers proved that this also holds for a stochastically perturbed KPP equation. The wave speed depends on the strength σ of the noise. The talk will be concerned with some conjectures and rigorous results about the behavior of the wave speed c(σ) as σ → 0 and σ → ∞.