Singular limit problems on the minimal travelling wave speed of the Lotka–Volterra competition model

Abstract

We investigate singular limits of the minimal travelling wave speed in a Lotka–Volterra competition-diffusion system. We identify several singular regimes and determine the corresponding speed selection mechanisms. The main difficulty arises from the lack of monotonicity of the minimal speed with respect to the diffusion rate and the intrinsic growth rate. Our approach relies on the comparison principle, the construction of carefully designed super-solutions and compactness arguments. These results provide a complete picture of how singular limits govern the transition between linear and nonlinear speed selection mechanisms.