scholarly journals The diffusive logistic model with a free boundary in heterogeneous environment

2014 ◽  
Vol 256 (6) ◽  
pp. 1927-1954 ◽  
Author(s):  
Peng Zhou ◽  
Dongmei Xiao
Keyword(s):  
Free Boundary ◽  
Logistic Model ◽  
Heterogeneous Environment

An evolutional free-boundary problem of a reaction–diffusion–advection system

2017 ◽  
Vol 147 (3) ◽  
pp. 615-648 ◽  
Author(s):  
Ling Zhou ◽  
Shan Zhang ◽  
Zuhan Liu
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Ecological Model ◽  
Reaction Diffusion ◽  
Spreading Speed ◽  
Heterogeneous Environment ◽  
Long Run ◽  
Strong Competition ◽  
Asymptotic Spreading

In this paper we consider a system of reaction–diffusion–advection equations with a free boundary, which arises in a competition ecological model in heterogeneous environment. The evolution of the free-boundary problem is discussed, which is an extension of the results of Du and Lin (Discrete Contin. Dynam. Syst. B19 (2014), 3105–3132). Precisely, when u is an inferior competitor, we prove that (u, v) → (0, V) as t→∞. When u is a superior competitor, we prove that a spreading–vanishing dichotomy holds, namely, as t→∞, either h(t)→∞ and (u, v) → (U, 0), or limt→∞h(t) < ∞ and (u, v) → (0, V). Moreover, in a weak competition case, we prove that two competing species coexist in the long run, while in a strong competition case, two species spatially segregate as the competition rates become large. Furthermore, when spreading occurs, we obtain some rough estimates of the asymptotic spreading speed.

scholarly journals A diffusive logistic model with a free boundary in time-periodic environment

2013 ◽  
Vol 265 (9) ◽  
pp. 2089-2142 ◽  
Author(s):  
Yihong Du ◽  
Zongming Guo ◽  
Rui Peng
Keyword(s):  
Free Boundary ◽  
Logistic Model ◽  
Periodic Environment ◽  
Time Periodic
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