A Fisher-KPP Model with a Nonlocal Weighted Free Boundary: Analysis of How Habitat Boundaries Expand, Balance or Shrink.

In this paper, we propose a novel free boundary problem to model the movement of single species with a range boundary. The spatial movement and birth/death processes of the species found within the range boundary are assumed to be governed by the classic Fisher-KPP reaction-diffusion equation, while the movement of a free boundary describing the range limit is assumed to be influenced by the weighted total population inside the range boundary and is described by an integro-differential equation. Our free boundary equation is a generalization of the classical Stefan problem that allows for nonlocal influences on the boundary movement so that range expansion and shrinkage are both possible.