Long-Time Behavior of a Reaction-Diffusion Model with Strong Allee Effect and Free Boundary: Effect of Protection Zone

This paper concerns the effect of the (separated/connected) protection zone for the evolution of an endangered species on the reaction-diffusion equation with the strong Allee effect and the free boundary. First, we describe the long-time dynamical behavior of the system of two types protection zones with the same length. Furthermore, the asymptotic profiles of solutions and the asymptotic spreading speed are estimated when spreading happens. Our results, together with those in previous papers Du et al. (J Differ Equ 266:7327-7356, 2019), Du and Lou (J Eur Math Soc 17:2673-2724, 2015) on two other closely related models, show that the protection zone and the free boundary play an important role in the evolution of the endangered species.