Stability of nonmonotone critical traveling waves for spatially discrete reaction-diffusion equations with time delay

被引：11

作者：

Tian, Ge ^{[1
]}

Zhang, Guobao ^{[1
]}

Yang, Zhaoxing ^{[1
]}

机构：

[1] Northwest Normal Univ, Coll Math & Stat, Lanzhou, Gansu, Peoples R China

来源：

TURKISH JOURNAL OF MATHEMATICS | 2017年 / 41卷 / 03期

关键词：

Spatially discrete reaction-diffusion equations; nonmonotone critical traveling waves; stability; weighted energy; LATTICE DIFFERENTIAL-EQUATIONS; NICHOLSONS BLOWFLIES EQUATION; MONOSTABLE NONLINEARITY; ASYMPTOTIC STABILITY; UNIQUENESS; EXISTENCE; DYNAMICS; FRONTS;

D O I：

10.3906/mat-1601-19

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is concerned with the existence and stability of critical traveling waves (waves with minimal speed c = c(*)) for a nonmonotone spatially discrete reaction-diffusion equation with time delay. We first show the existence of critical traveling waves by a limiting argument. Then, using the technical weighted energy method with some new variations, we prove that the critical traveling waves phi(x + c(*)t) (monotone or nonmonotone) are time-asymptotically stable when the initial perturbations are small in a certain weighted Sobolev norm.

引用

页码：655 / 680

页数：26

共 21 条

[1] Existence and asymptotic stability of traveling waves of discrete quasilinear monostable equations [J].

Chen, XF ;

Guo, JS .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2002, 184 (02) :549-569

[2] Uniqueness and asymptotics of traveling waves of monostable dynamics on lattices [J].

Chen, Xinfu ;

Fu, Sheng-Chen ;

Guo, Jong-Shenq .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2006, 38 (01) :233-258

[3] Stability of non-monotone critical traveling waves for reaction diffusion equations with time-delay [J].

Chern, I-Liang ;

Mei, Ming ;

Yang, Xiongfeng ;

Zhang, Qifeng .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 259 (04) :1503-1541

[4]

Guo JS, 2005, DISCRETE CONT DYN S, V12, P193

[5] Stability of travelling wavefronts in discrete reaction-diffusion equations with nonlocal delay effects [J].

Guo, Shangjiang ;

Zimmer, Johannes .

NONLINEARITY, 2015, 28 (02) :463-492

[6]

Guo SJ, ARXIV14065321V1

[7] Entire solutions for a discrete diffusive equation [J].

Guo, Yung-Jen Lin .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 347 (02) :450-458

[8] Spatial dynamics for lattice differential equations with a shifting habitat [J].

Hu, Changbing ;

Li, Bingtuan .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 259 (05) :1967-1989

[9] ASYMPTOTIC STABILITY OF NON-MONOTONE TRAVELING WAVES FOR TIME-DELAYED NONLOCAL DISPERSION EQUATIONS [J].

Huang, Rui ;

Mei, Ming ;

Zhang, Kaijun ;

Zhang, Qifeng .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2016, 36 (03) :1331-1353

[10] PLANAR TRAVELING WAVES FOR NONLOCAL DISPERSION EQUATION WITH MONOSTABLE NONLINEARITY [J].

Huang, Rui ;

Mei, Ming ;

Wang, Yong .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2012, 32 (10) :3621-3649

← 1 2 3 →