Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 269, Issue 2, Pages 1465-1483Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2020.01.011
Keywords
Competition-diffusion-advection; Homogeneous environment; Principal eigenvalue; Steady state; Global stability
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Funding
- Postdoctoral Science Foundation of China [2018M643281]
- Fundamental Research Funds for the Central Universities [19lgpy246]
- National Natural Science Foundation of China [11901596]
- NSERC of Canada
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In this paper, we mainly study a two-species competition model in a one-dimensional advective homogeneous environment, where the two species are identical except their diffusion rates. One interesting feature of the model is that the boundary condition at the downstream end represents a net loss of individuals, which is tuned by a parameter b to measure the magnitude of the loss. When the upstream end has the no-flux condition, Lou and Zhou (2015) [11] have confirmed that large diffusion rate is more favorable when 0 <= b < 1. Here we consider the case where the upstream end has the free-flow condition, which means that the upstream end is linked to a lake. We firstly investigate the corresponding single species model. Here we establish the existence and uniqueness of positive steady states. Then for the two-species model, we find that the parameter b can be regarded as a bifurcation parameter. Precisely, when 0 <= b < 1, large diffusion rate is more favorable while when b > 1, small diffusion rate is selected (if exists). When b = 1, the system is degenerate in the sense that there is a compact global attractor consisting of a continuum of steady states. (C) 2020 Elsevier Inc. All rights reserved.
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