A time-periodic diffusive prey–predator model with sign-changing growth rates and a free boundary. (April 2019)

• Record Type: Journal Article
• Authors: Huang, Haomin; Wang, Mingxin
• Is Part Of: Nonlinear analysis. Volume 46(2019)
• Page Start: 157
• Page End: 177
• Publication Date: 2019-04
• Subjects: Diffusive prey–predator model -- Heterogeneous time-periodic environment -- Sign-changing growth rates -- Free boundary -- Spreading and vanishing; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.09.013
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We undertake a study of a free boundary problem for a diffusive prey–predator model in the heterogeneous time-periodic environment, in which the local growth rates of two species may change signs and be very "negative" in a "suitable large region" (see the conditions (H1 ) and (H2 )). We investigate the spreading–vanishing dichotomy, long-time dynamical behavior of the solution, criteria for spreading and vanishing, and estimates of the asymptotic spreading speed of the free boundary. As an off-shoot of our analysis, we also obtain the existence of positive solutions to a T -periodic boundary value problem on half line associated with our free boundary problem.