Evolution of dispersal in advective homogeneous environments

Li Ma, ,College of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, Jiangxi, China, De Tang, ,School of Mathematics(Zhuhai), Sun Yat-sen University, Zhuhai 519082, Guangdong, China
2020 Discrete and Continuous Dynamical Systems. Series A  
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.
more » ... l Differential Equations, 55 (2016), Art. 137, 29 pp) considered the system under the noflux 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. 2020 Mathematics Subject Classification. Primary: 35K57, 35K61, 37C65, 92D25.
doi:10.3934/dcds.2020247 fatcat:jwqfdzolhzfwtcmxif4wy4d7si