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

TL;DR

This paper studies traveling wave solutions in a nonlocal reaction-diffusion model for populations structured by space and phenotype, identifying conditions for wave existence based on invasion speed.

Contribution

It establishes the existence of traveling waves with a minimal speed in a nonlocal population model, even when the principal eigenvalue is negative.

Findings

Existence of traveling waves for speeds c ≥ c*

Non-existence of waves for speeds c < c*

Identification of a minimal invasion speed c*

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