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

@inproceedings{Alfaro2012TravellingWI,
  title={Travelling waves in a nonlocal reaction-diffusion equation as a model for a population structured by a space variable and a phenotypic trait},
  author={Matthieu Alfaro and J{\'e}r{\^o}me Coville and Ga{\"e}l Raoul},
  year={2012}
}
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 ≥ c ∗ and the non existence when 0 ≤ c < c∗.