TITLE:
On Some Dynamics of a Diffusive Lotka-Volterra Competition-Advection System with Lethal Boundary Conditions
AUTHORS:
Dongxuan Zhao
KEYWORDS:
Global Asymptotic Stability, Competing Systems, Positive Steady-State Solution, Coexistence
JOURNAL NAME:
Applied Mathematics,
Vol.12 No.4,
April
19,
2021
ABSTRACT: In this paper, we mainly study a diffusive Lotka-Volterra competition-advection system with lethal boundary conditions in a general heterogeneous environment. By using the basic theory of partial differential equations and some nonlinear analysis techniques, we investigate the existence, uniqueness and global asymptotic behavior of steady-state solutions of the system equations. The existence, uniqueness and global asymptotic behavior of steady-state solutions are proved by upper and lower solutions, maximum principle and other methods. In theory, the methods and skills to deal with this kind of nonlinear problem are further developed, which provides a theoretical basis for understanding some practical problems.