Travelling waves in a nonlocal reaction-diffusion equation as a model for a population structured by a space variable and a phenotypical trait

Matthieu Alfaro (1) , Jérôme Coville (2) , Gaël Raoul (3)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 BioSP - Biostatistique et Processus Spatiaux
3 CEFE - Centre d’Ecologie Fonctionnelle et Evolutive

We consider a nonlocal reaction-diffusion equation as a model for a population structured by a space variable and a phenotypical trait. To sustain the possibility of invasion in the case where an underlying principal eigenvalue is negative, we investigate the existence of travelling wave solutions. We identify a minimal speed $c^*>0$, and prove the existence of waves when $c\geq c^*$ and the non existence when $0\leq c < c^*$

Mots clés: travelling waves; nonlocal reaction-diffusion equation

Mots clés: structured population

Domaines: Equations aux dérivées partielles [math.AP]

Matthieu Alfaro, Jérôme Coville, Gaël Raoul. Travelling waves in a nonlocal reaction-diffusion equation as a model for a population structured by a space variable and a phenotypical trait. Communications in Partial Differential Equations, 2013, 38 (12), pp.2126-2154. ⟨10.1080/03605302.2013.828069⟩. ⟨hal-00751647v2⟩