Pulsating fronts for nonlocal dispersion and KPP nonlinearity
Annales de l'I.H.P. Analyse non linéaire, Volume 30 (2013) no. 2, p. 179-223
In this paper we are interested in propagation phenomena for nonlocal reaction–diffusion equations of the type: u t=Ju-u+f(x,u)t,x 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 : https://doi.org/10.1016/j.anihpc.2012.07.005
Classification:  45C05,  45G10,  45M15,  45M20,  92D25
Keywords: Periodic front, Nonlocal dispersal, KPP nonlinearity
@article{AIHPC_2013__30_2_179_0,
     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},
     publisher = {Elsevier},
     volume = {30},
     number = {2},
     year = {2013},
     pages = {179-223},
     doi = {10.1016/j.anihpc.2012.07.005},
     zbl = {1288.45007},
     mrnumber = {3035974},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2013__30_2_179_0}
}
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://www.numdam.org/item/AIHPC_2013__30_2_179_0/

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