KPP traveling waves in the half-space

Reaction–diffusion equations are widely used to model spatial propagation, and constant-speed "traveling waves" play a central role in their dynamics. These waves are well understood in "essentially 1D" domains like cylinders, but much less is known about waves with noncompact transverse structure. In this direction, we will consider traveling waves of the KPP reaction–diffusion equation in the Dirichlet half-space. We will see that minimal-speed waves are unique (unlike faster waves) and exhibit curious asymptotics. The arguments rest on potential theory, the maximum principle, and a powerful connection with the probabilistic system known as branching Brownian motion.

This is joint work with Julien Berestycki, Yujin H. Kim, and Bastien Mallein.