Propagation in a fractional reaction-diffusion equation in a periodically hostile environment

Alexis Léculier (1) , Sepideh Mirrahimi (1) , Jean-Michel Roquejoffre (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We provide an asymptotic analysis of a fractional Fisher-KPP type equation in periodic non-connected 1-dimensional media with Dirichlet conditions outside the domain. After demonstrating the existence and uniqueness of a non-trivial bounded stationary state $n_+$ , we prove that the stable state $n_+$ invades the unstable state 0 with a speed which is exponential in time.

Mots clés: asymptotic analysis; exponential speed of propagation; Fisher KPP; Non-local fractional operator; perturbed test function

Domaines: Equations aux dérivées partielles [math.AP]

Alexis Léculier, Sepideh Mirrahimi, Jean-Michel Roquejoffre. Propagation in a fractional reaction-diffusion equation in a periodically hostile environment. 2019. ⟨hal-02124875v2⟩