Hopf bifurcation in a reaction-diffusion-advection model with nonlocal delay effect and Dirichlet boundary condition

In this paper, we investigate the dynamics of a reaction-diffusion-advection equation with nonlocal delay effect and Dirichlet boundary condition. The existence of spatially nonhomogeneous steady states and the associated Hopf bifurcation are obtained by using the Lyapunov-Schmidt reduction. We also give applications of the theoretical results to models with a logistic growth rate and a weak Allee growth rate.