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: ∂u ∂t = J ∗ u −u+ f (x,u) t ∈ R, x ∈ RN, 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.