Tính ổn định của các sóng lan truyền không đơn điệu trong phương trình khuếch tán rời rạc với phi tuyến tích chập đơn bền

Aguerrea M, Gomez C, Trofimchuk S. On uniqueness of semi-wavefronts. Math Ann, 2012, 354: 73–109 Chen X, Fu S C, Guo J S. Uniqueness and asymptotics of traveling waves of monostable dynamics on lattices. SIAM J Math Anal, 2006, 38: 233–258 Chen X, Guo J S. Existence and asymptotic stability of traveling waves of discrete quasilinear monostable equations. J Differential Equations, 2002, 184: 549–569 Chern I L, Mei M, Yang X, et al. Stability of non-monotone critical traveling waves for reaction-diffusion equations with time-delay. J Differential Equations, 2015, 259: 1503–1541 Diekmann O, Kaper H G. On the bounded solutions of a nonlinear convolution equation. Nonlinear Anal, 1978, 2: 721–737 Fang J, Wei J, Zhao X Q. Spreading speeds and travelling waves for non-monotone time-delayed lattice equations. Proc R Soc Lond Ser A Math Phys Eng Sci, 2010, 466: 1919–1934 Fang J, Wei J, Zhao X Q. Uniqueness of traveling waves for nonlocal lattice equations. Proc Amer Math Soc, 2011, 139: 1361–1373 Guo J S, Lin Y C. Traveling wave solution for a lattice dynamical system with convolution type nonlinearity. Discrete Contin Dyn Syst, 2012, 32: 101–124 Guo J S, Lin Y C. Entire solutions for a discrete diffusive equation with bistable convolution type nonlinearity. Osaka J Math, 2013, 50: 607–629 Guo J S, Morita Y. Entire solutions of reaction-diffusion equations and an application to discrete diffusive equations. Discrete Contin Dyn Syst, 2005, 12: 193–212 Guo S, Zimmer J. Stability of travelling wavefronts in discrete reaction-diffusion equations with nonlocal delay effects. Nonlinearity, 2015, 28: 463–492 Guo Y J L. Entire solutions for a discrete diffusive equation. J Math Anal Appl, 2008, 347: 450–458 Hu C, Li B. Spatial dynamics for lattice differential equations with a shifting habitat. J Differential Equations, 2015, 259: 1967–1989 Huang R, Mei M, Zhang K J, et al. Asymptotic stability of non-monotone traveling waves for time-delayed nonlocal dispersion equations. Discrete Contin Dyn Syst, 2016, 36: 1331–1353 Lin C K, Lin C T, Lin Y, et al. Exponential stability of non-monotone traveling waves for Nicholson’s blow ies equation. SIAM J Math Anal, 2014, 46: 1053–1084 Ma S. Traveling waves for non-local delayed diffusion equations via auxiliary equations. J Differential Equations, 2007, 237: 259–277 Ma S, Weng P, Zou X. Asymptotic speed of propagation and traveling wavefronts in a non-local delayed lattice differential equation. Nonlinear Anal, 2006, 65: 1858–1890 Ma S, Zou X. Existence, uniqueness and stability of travelling waves in a discrete reaction-diffusion monostable equation with delay. J Differential Equations, 2005, 217: 54–87 Ma S, Zou X. Propagation and its failure in a lattice delayed differential equation with global interaction. J Differential Equations, 2005, 212: 129–190 Mei M, So J W H. Stability of strong travelling waves for a non-local time-delayed reaction-diffusion equation. Proc Roy Soc Edinburgh Sect A, 2008, 138: 551–568 Mei M, So J W H, Li M Y, et al. Asymptotic stability of travelling waves for Nicholson’s blow ies equation with diffusion. Proc Roy Soc Edinburgh Sect A, 2004, 134: 579–594 Shigesada N, Kawasaki K. Biological Invasions: Theory and Practice. Oxford Series in Ecology and Evolution. New York: Oxford University Press, 1997 Shorrocks B, Swingland I R. Living in a Patch Environment. New York: Oxford University Press, 1990 Tian G, Zhang G B. Stability of traveling wavefronts for a discrete diffusive Lotka-Volterra competition system. J Math Anal Appl, 2017, 447: 222–242 Tian G, Zhang G B, Yang Z X. Stability of non-monotone critical traveling waves for spatially discrete reaction-diffusion equations with time delay. Turkish J Math, 2017, 41: 655–680 Weng P, Huang H X, Wu J H. Asymptotic speed of propagation of wave fronts in a lattice delay differential equation with global interaction. IMA J Appl Math, 2003, 68: 409–439 Yang Z X, Zhang G B, Tian G, et al. 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 Yu Z X. Uniqueness of critical traveling waves for nonlocal lattice equations with delays. Proc Amer Math Soc, 2012, 140: 3853–3859 Zhang G B, Ma R. Spreading speeds and traveling waves for a nonlocal dispersal equation with convolution-type crossing-monostable nonlinearity. Z Angew Math Phys, 2014, 65: 819–844