A DIFFUSIVE LOGISTIC PROBLEM WITH A FREE BOUNDARY IN TIME-PERIODIC ENVIRONMENT: FAVORABLE HABITAT OR UNFAVORABLE HABITAT

作者：Chen, Qiaoling^*; Li, Fengquan; Wang, Feng

来源：Discrete and Continuous Dynamical Systems-Series B, 2016, 21(1): 13-35.

DOI：10.3934/dcdsb.2016.21.13

• Diffusive logistic problem
• free boundary
• favorable habitat and unfavorable habitat
• periodic environment
• spreading-vanishing dichotomy
• sharp criteria

We study a diffusive logistic equation with a free boundary in time-periodic environment. To understand the effect of the diffusion rate d, the original habitat radius hp, the spreading capability it, and the initial density up on the dynamics of the problem, we divide the time-periodic habitat into two cases: favorable habitat and unfavorable habitat. By choosing d, h(0), mu and u(0) as variable parameters, we obtain a spreading-vanishing dichotomy and sharp criteria for the spreading and vanishing in time-periodic environment. We introduce the principal eigenvalue lambda(1)(d, alpha-gamma, h(0), T) to determine the spreading and vanishing of the invasive species. We prove that if lambda(1)(d, alpha-gamma, h(0), T) <= 0, the spreading must happen; while if lambda(1)(d, alpha-gamma, h(0),T) > 0, the spreading is also possible. Our results show that the species in the favorable habitat can establish itself if the diffusion rate is small or the occupying habitat is large. In an unfavorable habitat, the species vanishes if the initial density of the species is small. Moreover, when spreading occurs, the asymptotic spreading speed of the free boundary is determined.

• 出版日期2016-1
• 单位大连理工大学