Asymptotic patterns of a structured population diffusing in a two-dimensional strip

In this paper, we derive a population model for the growth of a single species on a two-dimensional strip with Neumann and Robin boundary conditions. We show that the dynamics of the mature population is governed by a reaction–diffusion equation with delayed global interaction. Using the theory of asymptotic speed of spread and monotone traveling waves for monotone semiflows, we obtain the spreading speed c^∗$c^{\ast }$, the non-existence of traveling waves with wave speed 0<c<c^∗$0<c<c^{\ast }$, and the existence of monotone traveling waves connecting the two equilibria for c≥c^∗$c\ge c^{\ast }$.