Global stability of traveling waves for a spatially discrete diffusion system with time delay

  • Received: 01 September 2020 Revised: 01 November 2020 Published: 11 January 2021
  • Primary: 35K57, 35B35; Secondary: 92D30

  • This article deals with the global stability of traveling waves of a spatially discrete diffusion system with time delay and without quasi-monotonicity. Using the Fourier transform and the weighted energy method with a suitably selected weighted function, we prove that the monotone or non-monotone traveling waves are exponentially stable in $ L^\infty(\mathbb{R})\times L^\infty(\mathbb{R}) $ with the exponential convergence rate $ e^{-\mu t} $ for some constant $ \mu>0 $.

    Citation: Ting Liu, Guo-Bao Zhang. Global stability of traveling waves for a spatially discrete diffusion system with time delay[J]. Electronic Research Archive, 2021, 29(4): 2599-2618. doi: 10.3934/era.2021003

    Related Papers:

  • This article deals with the global stability of traveling waves of a spatially discrete diffusion system with time delay and without quasi-monotonicity. Using the Fourier transform and the weighted energy method with a suitably selected weighted function, we prove that the monotone or non-monotone traveling waves are exponentially stable in $ L^\infty(\mathbb{R})\times L^\infty(\mathbb{R}) $ with the exponential convergence rate $ e^{-\mu t} $ for some constant $ \mu>0 $.



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    [1] Existence and asymptotic stability of traveling waves of discrete quasilinear monostable equations. J. Differential Equations (2002) 184: 549-569.
    [2] Stability of traveling wavefronts for a discrete diffusive competition system with three species. J. Math. Anal. Appl. (2019) 474: 909-930.
    [3] Stability of non-monotone critical traveling waves for reaction-diffusion equations with time-delay. J. Differential Equations (2015) 259: 1503-1541.
    [4] Wavefronts and global stability in a time-delayed population model with stage structure. R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. (2003) 459: 1563-1579.
    [5] Stability of traveling wavefronts in discrete reaction-diffusion equations with nonlocal delay effects. Nonlinearity (2015) 28: 463-492.
    [6] Traveling wave solutions for delayed lattice reaction-diffusion systems. IMA J. Appl. Math. (2015) 80: 302-323.
    [7] Existence and exponential stability of traveling waves for delayed reaction-diffusion systems. Nonlinearity (2018) 31: 838-863.
    [8] Spatial dynamics for lattice differential equations with a shifting habitat. J. Differential Equations (2015) 259: 1967-1989.
    [9] Y. Li, W.-T. Li and Y.-R. Yang, Stability of traveling waves of a diffusive susceptible-infective-removed (SIR) epidemic model, J. Math. Phys., 57 (2016), 041504, 28 pp. doi: 10.1063/1.4947106
    [10] Exponential stability of nonmonotone traveling waves for Nicholson's blowflies equation. SIAM J. Math. Anal. (2014) 46: 1053-1084.
    [11] Multidimensional stability of planar traveling waves for the delayed nonlocal dispersal competitive Lotka-Volterra system. Commu. Pure Appl. Anal. (2019) 18: 2069-2091.
    [12] Traveling wavefronts for time-delayed reaction-diffusion equation: (I) local nonlinearity. J. Differential Equations (2009) 247: 495-510.
    [13] Stability of strong traveling waves for a nonlocal time-delayed reaction-diffusion equation. Proc. Roy. Soc. Edinburgh Sect. A (2008) 138: 551-568.
    [14] Asymptotic stability of traveling waves for the Nicholson's blowflies equation with diffusion. Proc. Roy. Soc. Edinburgh Sect. A (2004) 134: 579-594.
    [15] Global stability of traveling waves with oscillations for time-delayed reaction-diffusion equations. Int. J. Numer. Anal. Model. (2019) 16: 375-397.
    [16] Global asymptotical stability of traveling waves in delayed reaction-diffusion equations. SIAM J. Math. Anal. (2000) 31: 514-534.
    [17] Global stability of non-monotone noncritical traveling waves for a discrete diffusion equation with a convolution type nonlinearity. Taiwanese J. Math. (2020) 24: 937-957.
    [18] S. Su and G.-B. Zhang, Global stability of traveling waves for delay reaction-diffusion systems without quasi-momotonicity, Electron. J. Differential Equations, (2020), Paper No. 46, 18 pp.
    [19] Stability of traveling wavefronts for a discrete diffusive Lotka-Volterra competition system. J. Math. Anal. Appl. (2017) 447: 222-242.
    [20] Stability of nonmonotone critical traveling waves for spatially discrete reaction-diffusion equations with time delay. Turkish J. Math. (2017) 41: 655-680.
    [21] Existence and uniqueness of traveling waves for non-monotone integral equations with application. J. Math. Anal. Appl. (2010) 365: 729-741.
    [22] Asymptotic stability of traveling waves for delayed reaction-diffusion equations with crossing-monostability. Z. Angew. Math. Phys. (2011) 62: 377-397.
    [23] Theoretical and numerical studies on global stability of traveling waves with oscillation for time-delayed nonlocal dispersion equations. Int. J. Numer. Anal. Model. (2020) 17: 68-86.
    [24] Stability of traveling waves in a monostable delayed system without quasi-monotonicity. Nonlinear Anal. Real World Appl. (2013) 14: 1511-1526.
    [25] Stability of non-monotone traveling waves for a discrete diffusion equation with monostable convolution type nonlinearity. Sci. China Math. (2018) 61: 1789-1806.
    [26] Stability of non-monotone non-critical traveling waves in discrete reaction-diffusion equations with time delay. Discrete Contin. Dyn. Syst. Ser. S (2017) 10: 581-603.
    [27] Z. Yu and C.-H. Hsu, Wave propagation and its stability for a class of discrete diffusion systems, Z. Angew. Math. Phys., 71 (2020), 194. doi: 10.1007/s00033-020-01423-4
    [28] Global stability of non-monotone traveling wave solutions for a nonlocal dispersal equation with time delay. J. Math. Anal. Appl. (2019) 475: 605-627.
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