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.
Cite this article
Juan Dávila, Salomé Martínez, Jérôme Coville, Pulsating fronts for nonlocal dispersion and KPP nonlinearity. Ann. Inst. H. Poincaré Anal. Non Linéaire 30 (2013), no. 2, pp. 179–223DOI 10.1016/J.ANIHPC.2012.07.005