The effect of protection zone on asymptotic dynamics of a reaction–diffusion model with a free boundary or unbounded boundary. (December 2022)

• Record Type: Journal Article
• Authors: Li, Jingjing; Sun, Ningkui
• Is Part Of: Nonlinear analysis. Volume 68(2022)
• Publication Date: 2022-12
• Subjects: Reaction–diffusion equation -- Protection zone -- Long time behavior -- Free boundary problem; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103697
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper is to investigate the effect of the protection zone for the evolution of a single species on the reaction–diffusion equations in the half-space or a free boundary domain. In the first part of this paper, we consider the previous case and obtain that only spreading happens for solutions of reaction–diffusion models on the half-line [ 0, ∞ ) . The second part of this paper is devoted to establishing the spreading-vanishing dichotomy for solutions of reaction–diffusion models with a free boundary. Moreover, by introducing a parameter σ in the initial data, we prove the sharp threshold behaviors. This paper can be regarded as a valuable complement to some existing research papers in this direction, for instance, Du et al. (2019) and Sun and Lei (2021).