Pulsating fronts for nonlocal dispersion and KPP nonlinearity
Juan Dávila
Departamento de Ingeniería Matemática and CMM, Universidad de Chile, Casilla 170 Correo 3, Santiago, ChileSalomé Martínez
Departamento de Ingeniería Matemática and CMM, Universidad de Chile, Casilla 170 Correo 3, Santiago, ChileJérôme Coville
INRA, Equipe BIOSP, Centre de Recherche dʼAvignon, Domaine Saint Paul, Site Agroparc, 84914 Avignon cedex 9, France
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Abstract
In this paper we are interested in propagation phenomena for nonlocal reaction–diffusion equations of the type:
where is a probability density and is a KPP nonlinearity periodic in the variables. Under suitable assumptions we establish the existence of pulsating fronts describing the invasion of the 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.
Cite this article
Juan Dávila, Salomé Martínez, Jérôme Coville, Pulsating fronts for nonlocal dispersion and KPP nonlinearity. Ann. Inst. H. Poincaré Anal. Non Linéaire 30 (2013), no. 2, pp. 179–223
DOI 10.1016/J.ANIHPC.2012.07.005