Evolution of dispersal in advective homogeneous environments

Li Ma; De Tang

doi:10.3934/dcds.2020247

Article Contents

2020, Volume 40, Issue 10: 5815-5830. Doi: 10.3934/dcds.2020247

This issue Previous Article Entropies of commuting transformations on Hilbert spaces Next Article Existence of positive solutions of Schrödinger equations with vanishing potentials

Evolution of dispersal in advective homogeneous environments

Li Ma^1, and
De Tang^2, ,

1.
College of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, Jiangxi, China
2.
School of Mathematics(Zhuhai), Sun Yat-sen University, Zhuhai 519082, Guangdong, China

^* Corresponding author
^* Corresponding author

Received: September 2019

Revised: February 2020

Published: June 2020

The first author is supported by the National Natural Science Foundation of China(Nos. 11801089, 11901110) and the second author is supported by the Postdoctoral Science Foundation of China(No.2018M643281), the Fundamental Research Funds for the Central Universities (No. 191gpy246) and National Natural Science Foundation of China(No. 11901596)

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Abstract

The effects of weak and strong advection on the dynamics of reaction-diffusion models have long been investigated. In contrast, the role of intermediate advection still remains poorly understood. This paper is devoted to studying a two-species competition model in a one-dimensional advective homogeneous environment, where the two species are identical except their diffusion rates and advection rates. Zhou (P. Zhou, On a Lotka-Volterra competition system: diffusion vs advection, Calc. Var. Partial Differential Equations, 55 (2016), Art. 137, 29 pp) considered the system under the no-flux boundary conditions. It is pointed that, in this paper, we focus on the case where the upstream end has the Neumann boundary condition and the downstream end has the hostile condition. By employing a new approach, we firstly determine necessary and sufficient conditions for the persistence of the corresponding single species model, in forms of the critical diffusion rate and critical advection rate. Furthermore, for the two-species model, we find that (i) the strategy of slower diffusion together with faster advection is always favorable; (ii) two species will also coexist when the faster advection with appropriate faster diffusion.

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Mathematics Subject Classification: Primary:35K57, 35K61, 37C65, 92D25.

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