Asymptotic behavior of solutions of a reaction–diffusion model with a protection zone and a free boundary. (September 2020)

• Record Type: Journal Article
• Authors: Sun, Ningkui; Han, Xuemei
• Is Part Of: Applied mathematics letters. Volume 107(2020)
• Publication Date: 2020-09
• Subjects: Reaction–diffusion equation -- Protection zone -- Long time behavior -- Free boundary problem; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2020.106470
• Languages: English
• ISSNs: 0893-9659

Abstract

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 ∗ .