TRAVELING WAVE SOLUTIONS FOR TIME PERIODIC REACTION-DIFFUSION SYSTEMS

被引：27
|
作者：
Bo, Wei-Jian [1 ]
Lin, Guo [1 ]
Ruan, Shigui [2 ]
机构：
[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China
[2] Univ Miami, Dept Math, Coral Gables, FL 33146 USA
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2018年 / 38卷 / 09期
基金：
美国国家科学基金会;
关键词：
Super- and sub-solutions; asymptotic behavior; Lotka-Volterra competitive system; FISHER-KPP EQUATION; SPREADING SPEEDS; VARIATIONAL PRINCIPLE; MONOTONE SEMIFLOWS; DYNAMICAL-SYSTEMS; PROPAGATION; STABILITY; EXISTENCE; ADVECTION; FRONTS;
D O I：
10.3934/dcds.2018189
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper deals with traveling wave solutions for time periodic reaction-diffusion systems. The existence of traveling wave solutions is established by combining the fixed point theorem with super- and sub-solutions, which reduces the existence of traveling wave solutions to the existence of super- and sub-solutions. The asymptotic behavior is determined by the stability of periodic solutions of the corresponding initial value problems. To illustrate the abstract results, we investigate a time periodic Lotka-Volterra system with two species by presenting the existence and nonexistence of traveling wave solutions, which connect the trivial steady state to the unique positive periodic solution of the corresponding kinetic system.
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页码：4329 / 4351
页数：23
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