Boundedness and persistence of populations in advective Lotka-Volterra competition system

Qi Wang; Yang Song; Lingjie Shao

doi:10.3934/dcdsb.2018195

Article Contents

2018, Volume 23, Issue 6: 2245-2263. Doi: 10.3934/dcdsb.2018195

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Boundedness and persistence of populations in advective Lotka-Volterra competition system

Department of Mathematics, Southwestern University of Finance and Economics, 555 Liutai Ave, Wenjiang, Chengdu, Sichuan 611130, China

* Corresponding author.QW is partially supported by NSF-China (Grant No. 11501460) and the Fundamental Research Funds for the Central Universities (Grant No. JBK1801062)
* Corresponding author.QW is partially supported by NSF-China (Grant No. 11501460) and the Fundamental Research Funds for the Central Universities (Grant No. JBK1801062)

Received: September 2016

Revised: April 2018

Early access: June 2018

Published: June 2018

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Abstract

We are concerned with a two-component reaction-advection-diffusion Lotka-Volterra competition system with constant diffusion rates subject to homogeneous Neumann boundary conditions. We first prove the global existence and uniform boundedness of positive classical solutions to this system. This result complements some of the global existence results in [Y. Lou, M. Winkler and Y. Tao, SIAM J. Math. Anal., 46 (2014), 1228-1262.], where one diffusion rate is taken to be a linear function of the population density. Our second result proves that the total population of each species admits a positive lower bound, under some conditions of system parameters (e.g., when the intraspecific competition rates are large). This result of population persistence indicates that the two competing species coexist over the habitat in a long time.

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Mathematics Subject Classification: Primary: 35K51, 92D25, 92D40.

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