Velocity enhancement of reaction-diffusion fronts by a line of fast diffusion

Laurent Dietrich (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We study the velocity of travelling waves of a reaction-diffusion system coupling a standard reaction-diffusion equation in a strip with a one-dimensional diffusion equation on a line. We show that it grows like the square root of the diffusivity on the line. This generalises a result of Berestycki, Roquejoffre and Rossi in the context of Fisher-KPP propagation where the question could be reduced to algebraic computations. Thus, our work shows that this phenomenon is a robust one. The ratio between the asymptotic velocity and the square root of the diffusivity on the line is characterised as the unique admissible velocity for fronts of an hypoelliptic system, which is shown to admit a travelling wave profile.

Mots clés: Reaction Diffusion; Waves propagation speed; Traveling fronts

Domaines: Equations aux dérivées partielles [math.AP]

Laurent Dietrich. Velocity enhancement of reaction-diffusion fronts by a line of fast diffusion. Transactions of the American Mathematical Society, 2017, 369, pp.3221-3252. ⟨10.1090/tran/6776⟩. ⟨hal-01137472v2⟩