JournalsaihpcVol. 30, No. 2pp. 179–223

Pulsating fronts for nonlocal dispersion and KPP nonlinearity

  • Juan Dávila

    Departamento de Ingeniería Matemática and CMM, Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile
  • Salomé Martínez

    Departamento de Ingeniería Matemática and CMM, Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile
  • Jérôme Coville

    INRA, Equipe BIOSP, Centre de Recherche dʼAvignon, Domaine Saint Paul, Site Agroparc, 84914 Avignon cedex 9, France
Pulsating fronts for nonlocal dispersion and KPP nonlinearity cover
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Abstract

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

ut=Juu+f(x,u)tR,xRN,\frac{\partial u}{\partial t} = J⁎u−u + f(x,u)\:t \in \mathbb{R},\:x \in \mathbb{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.

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