Publication Cover
Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 6
256
Views
6
CrossRef citations to date
0
Altmetric
Articles

Stability of traveling wave fronts for delayed Belousov–Zhabotinskii models with spatial diffusion

, &
Pages 922-941 | Received 29 Apr 2018, Accepted 16 Aug 2018, Published online: 11 Sep 2018

References

  • Belousov B. A periodic reaction and its mechanism. Ref Radiat Med Medgiz. 1959:145.
  • Murray J. On traveling wave solutions in a model for Belousov–Zhabotinskii reaction. J Theor Biol. 1976;56:329–353. doi: 10.1016/S0022-5193(76)80078-1
  • Kanel Y. Existence of traveling–wave solution of the Belousov–Zhabotinskii system. J Differ Equ. 1990;26:652–660.
  • Kanel Y. Existence of traveling–wave type solutions for the Belousov–Zhabotinskii system of equations II. Sib Math J. 1991;32:390–400.
  • Volpert A, Volpert V, Volpert V. Travelling wave solutions of parabolic systems. Vol. 140. Providence (RI): American Mathematical Society; 1994. (Translations of mathematical monographs).
  • Troy W. The existence of traveling wave front solutions of a model of the Belousov–Zhabotinskii reaction. J Differ Equ. 1980;36:89–98. doi: 10.1016/0022-0396(80)90078-9
  • Ye Q, Wang M. Traveling wave front solutions of Noyes–field system for Belousov–Zhabotinskii reaction. Nonlinear Anal TMA. 1987;11:1289–1302. doi: 10.1016/0362-546X(87)90046-0
  • Zaikin A, Zhabotinskii A. Concentration wave propagation in two dimemsional liquid phase self oscillation system. Nature. 1970;225:535–537. doi: 10.1038/225535b0
  • Hale J, Verduyn Lunel S. Introduction functional differential equations. New York (NY): Springer-Verlag; 1993.
  • Wu J. Theory and applications of partial functional differential equations. New York (NY): Springer-Verlag; 1996.
  • Wu J, Zou X. Traveling wave fronts of reaction–diffusion systems with delay. J Dyn Differ Eqn. 2001;13:651–687. doi: 10.1023/A:1016690424892
  • Boumenir A, Nguyen V. Perron theorem in the monotone iteration method for traveling waves in delayed reaction–diffusion equations. J Differ Equ. 2006;244:1551–1570. doi: 10.1016/j.jde.2008.01.004
  • Lin G, Li W. Traveling wavefronts of Belousov–Zhabotinskii system with diffusion and delay. Appl Math Lett. 2009;22:341–346. doi: 10.1016/j.aml.2008.04.006
  • Ma S. Traveling wavefronts for delayed reaction–diffusion system via a fixed point theorem. J Differ Equ. 2001;171:294–314. doi: 10.1006/jdeq.2000.3846
  • Trofimchuk E, Pinto M, Trofimchuk S. Traveling waves for a model of the Belousov–Zhabotinsky reaction. J Differ Equ. 2013;254:3690–3714. doi: 10.1016/j.jde.2013.02.005
  • Kapitula T. On the stability of traveling waves in weighted L∞ spaces. J Differ Equ. 1994;112:179–215. doi: 10.1006/jdeq.1994.1100
  • Schaaf K. Asymptotic behavior and traveling wave solutions for parabolic functional–differential equations. Trans Amer Math Soc. 1987;302:587–615.
  • Sattinger D. On the stability of waves of nonlinear parabolic systems. Adv Math. 1976;22:312–355. doi: 10.1016/0001-8708(76)90098-0
  • Hsu C, Lin J, Yang T. Stability for monostable wave fronts of delayed lattice differential equations. J Dyn Differ Equ. 2017;29:323–342. doi: 10.1007/s10884-015-9447-9
  • Lv G, Wang M. Nonlinear stability of traveling wave fronts for delayed reaction diffusion equations. Nonlinearity. 2010;13:845–873. doi: 10.1088/0951-7715/23/4/005
  • Lv G, Wang M. Nonlinear stability of traveling wave fronts for delayed reaction diffusion systems. Nonlinear Anal RWA. 2012;13:1854–1865. doi: 10.1016/j.nonrwa.2011.12.013
  • Mei M, Lin C, Lin C, et al. Traveling wavefronts for time–delayed reaction–diffusion equation: (I) local nonlinearity. J Differ Equ. 2009;247:495–510. doi: 10.1016/j.jde.2008.12.026
  • Mei M, Lin C, Lin C, et al. Traveling wavefronts for time–delayed reaction–diffusion equation: (II) local nonlinearity. J Differ Equ. 2009;247:511–529. doi: 10.1016/j.jde.2008.12.020
  • Wu S, Li W, Liu S. Exponential stability of traveling fronts in monostable reaction–advection–diffusion equations with non–local delay. Discrete Contin Dyn Syst B. 2013;17:347–366. doi: 10.3934/dcdsb.2012.17.347
  • Yang Y, Li W, Wu S. Stability of traveling waves in a monostable delayed system without quasi–monotonicity. Nonlinear Anal RWA. 2013;3:1511–1526. doi: 10.1016/j.nonrwa.2012.10.015
  • Yang Y, Li W, Wu S. Exponential stability of traveling fronts in a diffusion epidemic system with delay. Nonlinear Anal RWA. 2011;12:1223–1234. doi: 10.1016/j.nonrwa.2010.09.017
  • Yu Z, Mei M. Uniqueness and stability of traveling waves for cellular neural networks with multiple delays. J Differ Equ. 2016;260:241–267. doi: 10.1016/j.jde.2015.08.037
  • Yu Z, Xu F, Zhang W. Stability of invasion traveling waves for a competition system with nonlocal dispersals. Appl Anal. 2016;96:1–19.
  • Chen X, Guo J. Existence and asymptotic stability of traveling waves of discrete quasilinear monostable equations. J Differ Equ. 2002;184:549–569. doi: 10.1006/jdeq.2001.4153
  • Ma S, Wu J. Existence, uniqueness and asymptotic stability of traveling wavefronts in a non–local delayed diffusion equation. J Dyn Diff Eqn. 2007;19:391–436. doi: 10.1007/s10884-006-9065-7
  • Ma S, Zou X. Existence, uniqueness and stability of traveling waves in a discrete reaction–diffusion monostable equations with delay. J Differ Equ. 2005;217:54–87. doi: 10.1016/j.jde.2005.05.004
  • Wang Z, Li W, Ruan S. Traveling fronts in monostable equations with nonlocal delayed effects. J Dyn Differ Eqn. 2008;20:573–607. doi: 10.1007/s10884-008-9103-8
  • Smith H, Zhao X. Global asymptotic stability of the traveling waves in delayed reaction–diffusion equations. SIAM J Math Anal. 2000;31:514–534. doi: 10.1137/S0036141098346785
  • Martin R, Smith H. Abstract functional–differential equations and reaction–diffusion systems. Trans Amer Math Soc. 1990;321:1–44.
  • Mei M, So J. Stability of strong traveling waves for a nonlocal time–delayed reaction–diffusion equation. Proc R Soc Edinb A. 2008;138:551–568. doi: 10.1017/S0308210506000333
  • Mei M, So J, Li M, et al. Asymptotic stability of travelling waves for Nicholson's blowflies equation with diffusion. Proc R Soc Edinb A. 2004;134:579–594. doi: 10.1017/S0308210500003358

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.