Improved bounds for reaction-diffusion propagation with a line of nonlocal diffusion

Anne-Charline Chalmin , Jean-Michel Roquejoffre (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We consider here a model of accelerating fronts, introduced in [2], consisting of one equation with nonlocal diffusion on a line, coupled via the boundary condition with a reaction-diffusion equation of the Fisher-KPP type in the upper half-plane. It was proved in [2] that the propagation is accelerated in the direction of the line exponentially fast in time. We make this estimate more precise by computing an explicit correction that is algebraic in time. Unexpectedly, the solution mimicks the behaviour of the solution of the equation linearised around the rest state 0 in a closer way than in the classical fractional Fisher-KPP model.

Domaines: Equations aux dérivées partielles [math.AP]

Anne-Charline Chalmin, Jean-Michel Roquejoffre. Improved bounds for reaction-diffusion propagation with a line of nonlocal diffusion. 2019. ⟨hal-02352796⟩