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; 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

Analysis of PDEs 2012-12-03 v2

Authors: Matthieu Alfaro , Jérôme Coville , Gaël Raoul

Abstract

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

Keywords

travelling waves nonlocal reaction-diffusion equation population dynamics phenotypical trait minimal speed principal eigenvalue

Cite

@article{arxiv.1211.3228,
  title  = {Travelling waves in a nonlocal reaction-diffusion equation as a model for a population structured by a space variable and a phenotypical trait},
  author = {Matthieu Alfaro and Jérôme Coville and Gaël Raoul},
  journal= {arXiv preprint arXiv:1211.3228},
  year   = {2012}
}

Related papers

View all related →