Pulsating fronts for nonlocal dispersion and KPP nonlinearity

Coville, Jérôme; Dávila, Juan; Martínez, Salomé

Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 2, pp. 179-223.

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

$$\frac{\partial u}{\partial t}=J⁎u-u+f(x,u)t\in ℝ,x\in {ℝ}^N,$$

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.

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