Pulsating fronts for nonlocal dispersion and KPP nonlinearity

In this paper we are interested in propagation phenomena for nonlocal reaction diffusion equations of the type: a It partial derivative u/partial derivative t = J * u - u + f(x,u) t is an element of R, x is an element of R-N, 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. (C) 2012 Elsevier Masson SAS. All rights reserved.