Pulsating fronts for nonlocal dispersion and KPP nonlinearity
Annales de l'I.H.P. Analyse non linéaire, Volume 30 (2013) no. 2, pp. 179-223.

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

 $\frac{\partial u}{\partial t}=J⁎u-u+f\left(x,u\right)\phantom{\rule{1em}{0ex}}t\in ℝ,\phantom{\rule{0.166667em}{0ex}}x\in {ℝ}^{N},$
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.

DOI: 10.1016/j.anihpc.2012.07.005
Classification: 45C05,  45G10,  45M15,  45M20,  92D25
Keywords: Periodic front, Nonlocal dispersal, KPP nonlinearity
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author = {Coville, J\'er\^ome and D\'avila, Juan and Mart{\'\i}nez, Salom\'e},
title = {Pulsating fronts for nonlocal dispersion and {KPP} nonlinearity},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {179--223},
publisher = {Elsevier},
volume = {30},
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Coville, Jérôme; Dávila, Juan; Martínez, Salomé. Pulsating fronts for nonlocal dispersion and KPP nonlinearity. Annales de l'I.H.P. Analyse non linéaire, Volume 30 (2013) no. 2, pp. 179-223. doi : 10.1016/j.anihpc.2012.07.005. http://archive.numdam.org/articles/10.1016/j.anihpc.2012.07.005/

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