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arXiv · 1302.1053

Pulsating fronts for nonlocal dispersion and KPP nonlinearity

Jerome Coville·Juan Davila·Salome Martinez
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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.

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Jerome Coville, Juan Davila, Salome Martinez. 2013-02-05. Pulsating fronts for nonlocal dispersion and KPP nonlinearity. https://doi.org/10.1016/j.anihpc.2012.07.005

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