Global dynamics for a class of reaction-diffusion equations with distributed delay and non-monotone bistable nonlinearity

This work is devoted to the study of the global dynamics for a class of reaction-diffusion equations with distributed delay and non-monotone bistable nonlinearity. By using a comparison result, we characterize the basins of attraction of each steady state, that is, the trivial one and two positive steady states. We apply our results to a diffusive blowflies model with Allee effect and distributed delay.