Dynamics of a Reaction–Diffusion–Advection System with Nonlinear Boundary Conditions

Abstract

In this paper, we consider a single-species reaction–diffusion–advection population model with nonlinear boundary condition in heterogenous space. We not only investigate the existence, nonexistence and stability of positive steady-state solutions through a linear elliptic eigenvalue problem by means of variational approach, but also verify the existence of steady-state bifurcations at zero solution through Crandall and Robinowitz bifurcation theory and discuss the stability of bifurcations, which can lead to Allee effect when the bifurcation is subcritical.