Using a new method of monotone iteration of a pair of smooth lower- and upper-solutions, the traveling wave solutions of the classical Lotka-Volterra system are shown to exist for a family of wave speeds. Such constructed upper and lower solution pair enables us to derive the explicit value of the minimal (critical) wave speed as well as the asymptotic rates of the wave solutions at infinities. Furthermore, the traveling wave corresponding to each wave speed is unique modulo a translation of the origin. The stability of the traveling wave solutions with non-critical wave speed is also studied by spectral analysis of the linearized operator in exponentially weighted Banach spaces.
Lotka-Volterra competition models on finite graphs
本文研究了有限连通图上三个两种群竞争的Lotka-Volterra竞争模型，分别具有Dirichlet、Neumann和无边界条件.在Neumann边界条件和无边界条件下，当时间趋于无穷大时，种群中的一个种群灭绝而另一个种群生存，或者两个竞争种群共存，这主要取决于种群竞争力的强弱和种群初始规模.我们的一个结果部分回答了斯拉夫·勒克在[SIAM J. Appl. Dyn.系统：19（2020）]。证明主要结果的关键技术是上、下解方法，本文针对有限图上的弱耦合抛物型方程组发展了上、下解方法。
Traveling Wave Solutions for Delayed Reaction-Diffusion Systems and Applications to Lotka-Volterra Competition-Diffusion Models with Distributed Delays
Propagation Direction of Bistable Traveling Fronts in the Lotka--Volterra Competition--Diffusion System
School of Mathematical Sciences, Shanghai Jiao Tong University（上海交通大学数学科学学院）；Institute of Natural Sciences, Shanghai Jiao Tong University（上海交通大学自然科学研究院）；Chern Institute of Mathematics, Nankai University（南开大学陈省身数学研究所）
Sharp Thresholds for Linear Determinacy and Zero Wave Speed in Lotka-Volterra Competition-Diffusion Systems
School of Mathematical Sciences, Shanghai Jiao Tong University（上海交通大学数学科学学院）；Institute of Natural Sciences, Shanghai Jiao Tong University（上海交通大学自然博物馆）；Chern Institute of Mathematics, Nankai University（南开大学陈省身数学研究所）
