Two kinds of free boundary problems for the diffusive prey–predator model. (August 2015)

• Record Type: Journal Article
• Authors: Wang, Mingxin; Zhang, Yang
• Is Part Of: Nonlinear analysis. Volume 24(2015)
• Page Start: 73
• Page End: 82
• Publication Date: 2015-08
• Subjects: Prey–predator model -- Free boundary problems -- Asymptotic behavior -- Criteria for spreading and vanishing; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2015.01.004
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper we study two kinds of free boundary problems for the diffusive prey–predator model over a one dimensional habitat, in which the free boundary represents the spreading front and is only caused by the prey. In these two problems, it is assumed that the species can only invade further into the new environment from the right end of the habitat, and the spreading front expands at a speed that is proportional to the prey's population gradient at the front. Asymptotic behaviors of solution as t → ∞ are discussed firstly. The acquired results can help us to comprehend whether the expanding is successful or not. Then we establish the criteria for spreading and vanishing.