Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 259, Issue 1, Pages 141-171Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2015.02.004
Keywords
Reaction-diffusion-advection; Competition; Persistence; Evolution of dispersal
Categories
Funding
- NSF grant [DMS-1411476]
- Recruitment Program of Global Experts
- NSFC [11371248]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1411476] Funding Source: National Science Foundation
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We consider a single species model and a two-species competition model in a one-dimensional advective homogeneous enviromnent. One interesting feature in these models concerns the boundary condition at the downstream end, where the species can be exposed to a net loss of individuals, as tuned by a parameter b which measures the magnitude of the loss. We first determine necessary and sufficient conditions for the persistence of a single species for general value of b, in terms of the critical habitat size and the critical advection rate. Then for the competition model, we assume that two species are identical except their random diffusion rates. We obtain complete understanding when 0 <= b 1, and our result indicates that larger diffusion rate is selected, extending an earlier work [20] (b = 1). However, for b > 1 the dynamics can be quite different, and particularly we illustrate that some intermediate diffusion rate may be. selected when b > 3/2. (C) 2015 Elsevier Inc. All rights reserved.
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