2013/01/10 by Mingxin Wang, Wang, Mingxin · 1 citation
Mathematics · #35B40 #35K51 #35R35 #92B05 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #G.1.8 #acm:35B40 #acm:35K51 #acm:35R35 #acm:92B05 #math.AP #math.CA #msc:35B40 #msc:35K51 #msc:35R35 #msc:92B05
paper · pdf · doi:10.48550/arxiv.1301.2063
28 pages
arxiv created 2014/01/13 · arxiv updated 2014/01/14
In this paper we investigate some free boundary problems for the Lotka-Volterra type prey-predator model in one space dimension. The main objective is to understand the asymptotic behavior of the two species (prey and predator) 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 solution and criteria for spreading and vanishing are also obtained. Finally, when spreading successfully, we provide an estimate to show that the spreading speed (if exists) cannot be faster than the minimal speed of traveling wavefront solutions for the prey-predator model on the whole real line without a free boundary.