Nonlocal anisotropic dispersal with monostable nonlinearity

Jérôme Coville (1) , Juan Davila (2, 3) , Salome Martinez (2, 3)

1 BioSP - Biostatistique et Processus Spatiaux
2 CMM - Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago]
3 DIM - Departamento de Ingeniería Matemática [Santiago]

We study the travelling wave problem J*u − u − cu' + f (u) = 0 in R, u(−∞) = 0, u(+∞) = 1 with an asymmetric kernel J and a monostable nonlinearity. We prove the existence of a minimal speed, and under certain hypothesis the uniqueness of the profile for c = 0. For c = 0 we show examples of nonuniqueness.

Mots clés: Integral equation; Nonlocal anisotropic dispersal; Travelling waves; KPP nonlinearity

Domaines: Equations aux dérivées partielles [math.AP]; Analyse classique [math.CA]

Jérôme Coville, Juan Davila, Salome Martinez. Nonlocal anisotropic dispersal with monostable nonlinearity. Journal of Differential Equations, 2008, 244, pp.3080-3118. ⟨10.1016/j.jde.2007.11.002⟩. ⟨hal-00602285⟩