Pulsating fronts for nonlocal dispersion and KPP nonlinearity

Abstract

In this paper we are interested in propagation phenomena for nonlocal reaction–diffusion equations of the type:

where $J$ is a probability density and $f$ is a KPP nonlinearity periodic in the $x$ variables. Under suitable assumptions we establish the existence of pulsating fronts describing the invasion of the $0$ state by a heterogeneous state. We also give a variational characterization of the minimal speed of such pulsating fronts and exponential bounds on the asymptotic behavior of the solution.