TRAVELING WAVE SOLUTIONS FOR TIME PERIODIC REACTION-DIFFUSION SYSTEMS

被引：28

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.

引用

页码：4329 / 4351

页数：23

共 53 条

[1] Periodic traveling waves and locating oscillating patterns in multidimensional domains [J].

Alikakos, ND ;

Bates, PW ;

Chen, XF .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 351 (07) :2777-2805

[2]

[Anonymous], ELECT J DIFFERENTIAL

[3]

[Anonymous], REACTION DIFFUSION W

[4]

[Anonymous], 2011, INTRO REACTION DIFFU

[5]

[Anonymous], 1995, Analytic semigroups and optimal regularity in parabolic problems

[6]

[Anonymous], ANN EUGENIC 4, DOI DOI 10.1111/j.1469-1809.1937.tb02153.x

[7]

Aronson D G., 1975, Lecture Notes in Math., ppp 5

[8] SPREADING SPEEDS AND TRAVELING WAVES FOR SPACE-TIME PERIODIC NONLOCAL DISPERSAL COOPERATIVE SYSTEMS [J].

Bao, Xiongxiong ;

Shen, Wenxian ;

Shen, Zhongwei .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2019, 18 (01) :361-396

[9] Existence and stability of time periodic traveling waves for a periodic bistable Lotka-Volterra competition system [J].

Bao, Xiongxiong ;

Wang, Zhi-Cheng .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 255 (08) :2402-2435

[10] Spreading speeds for one-dimensional monostable reaction-diffusion equations [J].

Berestycki, Henri ;

Nadin, Gregoire .

JOURNAL OF MATHEMATICAL PHYSICS, 2012, 53 (11)

← 1 2 3 4 5 6 →