# American Institute of Mathematical Sciences

August  2018, 23(6): 2245-2263. doi: 10.3934/dcdsb.2018195

## 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)

Received  September 2016 Revised  April 2018 Published  June 2018

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.

Citation: Qi Wang, Yang Song, Lingjie Shao. Boundedness and persistence of populations in advective Lotka-Volterra competition system. Discrete & Continuous Dynamical Systems - B, 2018, 23 (6) : 2245-2263. doi: 10.3934/dcdsb.2018195
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