1,366 research outputs found
On some Free Boundary Problems of the Prey-predator Model
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 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.Comment: 28 page
Dynamics for the diffusive Leslie-Gower model with double free boundaries
In this paper we investigate a free boundary problem for the diffusive
Leslie-Gower prey-predator model with double free boundaries in one space
dimension. This system models the expanding of an invasive or new predator
species in which the free boundaries represent expanding fronts of the predator
species. We first prove the existence, uniqueness and regularity of global
solution. Then provide a spreading-vanishing dichotomy, namely the predator
species either successfully spreads to infinity as at both fronts
and survives in the new environment, or it spreads within a bounded area and
dies out in the long run. The long time behavior of and criteria for
spreading and vanishing are also obtained. Because the term (which
appears in the second equation) may be unbounded when nears zero, it will
bring some difficulties for our study.Comment: 19 page
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