Stability of traveling wavefronts for time-delayed reaction-diffusion equations

Previous Article
On a solution with transition layers for a bistable reaction-diffusion equation with spatially heterogeneous environments
PROC Home
This Issue
Next Article
On the one-dimensional version of the dynamical Marguerre-Vlasov system with thermal effects

2009, 2009(Special): 526-535. doi: 10.3934/proc.2009.2009.526

Stability of traveling wavefronts for time-delayed reaction-diffusion equations

1.	Department of Mathematics, Champlain College Saint-Lambert, Saint-Lambert, Quebec, J4P 3P2

Received June 2008 Revised April 2009 Published September 2009

Abstract
Related Papers

This paper is concerned with time-delayed reaction-diffusion equations. For all traveling wavefronts, they are proved to be stable time-asymptotically by the technical weighted energy method with the comparison principle together, which extends the wave stability results obtained in [7,8]. Some numerical simulations are also carried out, which confirm our theoretical results.

Keywords: time-delayed reaction diffusion equations, stability, traveling wavefronts, Nicolson's blowflies equation.

Mathematics Subject Classification: Primary: 35K57; Secondary: 34K20, 92D25.

Citation: Ming Mei. Stability of traveling wavefronts for time-delayed reaction-diffusion equations. Conference Publications, 2009, 2009 (Special) : 526-535. doi: 10.3934/proc.2009.2009.526

[1]	Yicheng Jiang, Kaijun Zhang. Stability of traveling waves for nonlocal time-delayed reaction-diffusion equations. Kinetic & Related Models, 2018, 11 (5) : 1235-1253. doi: 10.3934/krm.2018048
[2]	Jianhua Huang, Xingfu Zou. Existence of traveling wavefronts of delayed reaction diffusion systems without monotonicity. Discrete & Continuous Dynamical Systems - A, 2003, 9 (4) : 925-936. doi: 10.3934/dcds.2003.9.925
[3]	Rui Huang, Ming Mei, Kaijun Zhang, Qifeng Zhang. Asymptotic stability of non-monotone traveling waves for time-delayed nonlocal dispersion equations. Discrete & Continuous Dynamical Systems - A, 2016, 36 (3) : 1331-1353. doi: 10.3934/dcds.2016.36.1331
[4]	Ming Mei, Yau Shu Wong. Novel stability results for traveling wavefronts in an age-structured reaction-diffusion equation. Mathematical Biosciences & Engineering, 2009, 6 (4) : 743-752. doi: 10.3934/mbe.2009.6.743
[5]	Yanbin Tang, Ming Wang. A remark on exponential stability of time-delayed Burgers equation. Discrete & Continuous Dynamical Systems - B, 2009, 12 (1) : 219-225. doi: 10.3934/dcdsb.2009.12.219
[6]	Shi-Liang Wu, Tong-Chang Niu, Cheng-Hsiung Hsu. Global asymptotic stability of pushed traveling fronts for monostable delayed reaction-diffusion equations. Discrete & Continuous Dynamical Systems - A, 2017, 37 (6) : 3467-3486. doi: 10.3934/dcds.2017147
[7]	Guangrui Li, Ming Mei, Yau Shu Wong. Nonlinear stability of traveling wavefronts in an age-structured reaction-diffusion population model. Mathematical Biosciences & Engineering, 2008, 5 (1) : 85-100. doi: 10.3934/mbe.2008.5.85
[8]	Qi An, Weihua Jiang. Spatiotemporal attractors generated by the Turing-Hopf bifurcation in a time-delayed reaction-diffusion system. Discrete & Continuous Dynamical Systems - B, 2019, 24 (2) : 487-510. doi: 10.3934/dcdsb.2018183
[9]	Zhao-Xing Yang, Guo-Bao Zhang, Ge Tian, Zhaosheng Feng. Stability of non-monotone non-critical traveling waves in discrete reaction-diffusion equations with time delay. Discrete & Continuous Dynamical Systems - S, 2017, 10 (3) : 581-603. doi: 10.3934/dcdss.2017029
[10]	Wei-Jie Sheng, Wan-Tong Li. Multidimensional stability of time-periodic planar traveling fronts in bistable reaction-diffusion equations. Discrete & Continuous Dynamical Systems - A, 2017, 37 (5) : 2681-2704. doi: 10.3934/dcds.2017115
[11]	Weijiu Liu. Asymptotic behavior of solutions of time-delayed Burgers' equation. Discrete & Continuous Dynamical Systems - B, 2002, 2 (1) : 47-56. doi: 10.3934/dcdsb.2002.2.47
[12]	Martin Gugat, Markus Dick. Time-delayed boundary feedback stabilization of the isothermal Euler equations with friction. Mathematical Control & Related Fields, 2011, 1 (4) : 469-491. doi: 10.3934/mcrf.2011.1.469
[13]	Cui-Ping Cheng, Wan-Tong Li, Zhi-Cheng Wang. Asymptotic stability of traveling wavefronts in a delayed population model with stage structure on a two-dimensional spatial lattice. Discrete & Continuous Dynamical Systems - B, 2010, 13 (3) : 559-575. doi: 10.3934/dcdsb.2010.13.559
[14]	Tarik Mohammed Touaoula. Global stability for a class of functional differential equations (Application to Nicholson's blowflies and Mackey-Glass models). Discrete & Continuous Dynamical Systems - A, 2018, 38 (9) : 4391-4419. doi: 10.3934/dcds.2018191
[15]	Xiaojie Hou, Wei Feng. Traveling waves and their stability in a coupled reaction diffusion system. Communications on Pure & Applied Analysis, 2011, 10 (1) : 141-160. doi: 10.3934/cpaa.2011.10.141
[16]	Zhaosheng Feng. Traveling waves to a reaction-diffusion equation. Conference Publications, 2007, 2007 (Special) : 382-390. doi: 10.3934/proc.2007.2007.382
[17]	Elena Trofimchuk, Manuel Pinto, Sergei Trofimchuk. Pushed traveling fronts in monostable equations with monotone delayed reaction. Discrete & Continuous Dynamical Systems - A, 2013, 33 (5) : 2169-2187. doi: 10.3934/dcds.2013.33.2169
[18]	Shi-Liang Wu, Wan-Tong Li, San-Yang Liu. Exponential stability of traveling fronts in monostable reaction-advection-diffusion equations with non-local delay. Discrete & Continuous Dynamical Systems - B, 2012, 17 (1) : 347-366. doi: 10.3934/dcdsb.2012.17.347
[19]	Xiaojie Hou, Yi Li. Local stability of traveling-wave solutions of nonlinear reaction-diffusion equations. Discrete & Continuous Dynamical Systems - A, 2006, 15 (2) : 681-701. doi: 10.3934/dcds.2006.15.681
[20]	Gabriela Planas, Eduardo Hernández. Asymptotic behaviour of two-dimensional time-delayed Navier-Stokes equations. Discrete & Continuous Dynamical Systems - A, 2008, 21 (4) : 1245-1258. doi: 10.3934/dcds.2008.21.1245

Impact Factor:

American Institute of Mathematical Sciences