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Pulsating fronts for nonlocal dispersion and KPP nonlinearity

Research paper by Jerome Coville, Juan Davila, Salome Martinez

Indexed on: 05 Feb '13Published on: 05 Feb '13Published in: Mathematics - Analysis of PDEs



Abstract

In this paper we are interested in propagation phenomena for nonlocal reaction-diffusion equations of the type: $\delta_tu = J \times u - u + f (x, u) t \in R^+, x \in R^N$, 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.