Travelling waves in nonlocal reaction-dispersion equations with diffuse L{é}vy measures

Abstract

In this paper, we focus on the existence of travelling fronts for nonlocal reaction-dispersion models. Our aim is to provide a unified existence proof in a very broad framework using simple real analysis tools. In particular, we review the existing literature and fill in the gaps. It appears that the central case is the bistable nonlinearity, which we then extend to other classical nonlinearities.