A reaction-diffusion-advection two-species competition system with a free boundary in heterogeneous environment

Bo Duan; Zhengce Zhang

doi:10.3934/dcdsb.2021067

Article Contents

2022, Volume 27, Issue 2: 837-861. Doi: 10.3934/dcdsb.2021067

This issue Previous Article Input-to-state stability of infinite-dimensional stochastic nonlinear systems Next Article Stability of hydrostatic equilibrium to the 2D fractional Boussinesq equations

A reaction-diffusion-advection two-species competition system with a free boundary in heterogeneous environment

Bo Duan and
Zhengce Zhang^,

School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, China

^* Corresponding author: Zhengce Zhang
^* Corresponding author: Zhengce Zhang

Received: September 30, 2020

Revised: December 31, 2020

Early access: March 2021

Published: February 2022

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Abstract

In this paper, we investigate a reaction-diffusion-advection two-species competition system with a free boundary in heterogeneous environment. The primary aim is to study the impact of small advection terms and heterogeneous environment, which is on two species' dynamics via a free boundary. The function $ m(x) $ represents heterogeneous environment, and it can satisfy positive everywhere condition or changeable sign condition. Firstly, on one hand, we provide long time behaviors of the solution in vanishing case when $ m(x) $ satisfies both conditions above; on the other hand, long time behaviors of the solution in spreading case are got when $ m(x) $ satisfies positive everywhere condition. Secondly, a spreading-vanishing dichotomy and several sufficient conditions through the initial data and the moving parameters are obtained to determine whether spreading or vanishing of two species happens when $ m(x) $ satisfies both conditions above. Furthermore, we derive estimates of spreading speed of the free boundary when $ m(x) $ satisfies positive everywhere condition and two species spreading occurs.

Keywords:

Reaction-diffusion-advection competition system,
free boundary,
heterogeneous environment,
spreading-vanishing dichotomy,
spreading speed.

Mathematics Subject Classification: Primary: 35B40, 35K51; Secondary: 35R35, 92B05.

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