Pulsating fronts for nonlocal dispersion and KPP nonlinearity

Coville, Jérôme; Dávila, Juan; Martínez, Salomé

Coville, Jérôme ; Dávila, Juan ; Martínez, Salomé

Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013), p. 179-223 / Harvested from Numdam

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Résumé

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

Publié le : 2013-01-01

MR 3035974 | Zbl 1288.45007

DOI : https://doi.org/10.1016/j.anihpc.2012.07.005
Classification: 45C05, 45G10, 45M15, 45M20, 92D25

@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},
     volume = {30},
     year = {2013},
     pages = {179-223},
     doi = {10.1016/j.anihpc.2012.07.005},
     mrnumber = {3035974},
     zbl = {1288.45007},
     language = {en},
     url = {http://dml.mathdoc.fr/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, Tome 30 (2013) pp. 179-223. doi : 10.1016/j.anihpc.2012.07.005. http://gdmltest.u-ga.fr/item/AIHPC_2013__30_2_179_0/

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