Asymptotic behavior of solutions of a reaction–diffusion model with a protection zone and a free boundary. (September 2020) - Sun, Ningkui; Han, Xuemei
Abstract: In this paper, we study the long time behavior of solutions of a reaction–diffusion model with a protection zone and a free boundary in one dimensional space. We prove that there exists a critical value L ∗ such that a vanishing–spreading dichotomy result holds when the length of the protection zone is smaller than L ∗ ; only spreading happens when the length of the protection zone is larger than L ∗ . This suggests that the protection zone works when its length is larger than the critical value L ∗ .