Pulsating fronts for nonlocal dispersion and KPP nonlinearity
Résumé
In this paper we are interested in propagation phenomena for nonlocal reaction-diffusion equations of the type: ∂_tu = J ∗ u − u + f (x, u) t ∈ R^+, x ∈ 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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