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) tεR,xεRN, 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. © 2012 Elsevier Masson SAS. All rights reserved.