2014/01/13 by Mingxin Wang, Jingfu Zhao
Mathematics · #acm:35B40 #acm:35K51 #acm:35R35 #acm:92B05 #math.AP #msc:35B40 #msc:35K51 #msc:35R35 #msc:92B05
paper · pdf · doi:10.1007/s10884-014-9363-4
19 pages. arXiv admin note: substantial text overlap with arXiv:1301.2063
arxiv created 2014/01/13 · arxiv updated 2015/06/18
In this paper we investigate two free boundary problems for a Lotka-Volterra type competition model in one space dimension. The main objective is to understand the asymptotic behavior of the two competing species spreading via a free boundary. We prove a spreading-vanishing dichotomy, namely the two species either successfully spread to the entire space as time t goes to infinity and survive in the new environment, or they fail to establish and die out in the long run. The long time behavior of the solutions and criteria for spreading and vanishing are also obtained. This paper is an improvement and extension of J. Guo and C. Wu.