Pulsating fronts for nonlocal dispersion and KPP nonlinearity

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Abstract

In this paper we are interested in propagation phenomena for nonlocal reaction-diffusion equations of the type:∂u/∂t=J*u-u+f(x,u) tεR,xεRN, 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. © 2012 Elsevier Masson SAS. All rights reserved.

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Coville, J., Dávila, J., & Martínez, S. (2013). Pulsating fronts for nonlocal dispersion and KPP nonlinearity. Annales de l’Institut Henri Poincare (C) Analyse Non Lineaire, 30(2), 179–223. https://doi.org/10.1016/j.anihpc.2012.07.005

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