Long-time behavior of a reaction-diffusion model with strong Allee effect and free boundary: effect of a protection zone

TL;DR

This study investigates how protection zones influence the long-term dynamics and spreading speed of an endangered species modeled by a reaction-diffusion equation with a strong Allee effect and free boundary, highlighting the importance of these zones.

Contribution

It provides a detailed analysis of the long-time behavior and asymptotic profiles of solutions in models with protection zones, extending previous work on related models.

Findings

Protection zones significantly affect species survival and spread.

Asymptotic spreading speed can be estimated under different protection zone configurations.

Protection zones and free boundaries are crucial in species conservation modeling.

Abstract

This paper concerns the effect of the (separated/connected) protection zone for the evolution of an endangered species on the reaction-diffusion equation with strong Allee effect and free boundary. We give a description of the long-time dynamical behavior of the problem 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 [8, 12] 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.