Browse Journals

[1] M. Aguerrea, S. Trofimchuk and G. Valenzuela, Uniqueness of fast travelling fronts in reaction-diffusion equations with delay, Proceedings of the Royal Society of London: Series A 464(2098) (2008), 2591-2608.

DOI: https://doi.org/10.1098/rspa.2008.0011

[2] X. Chen, Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations, Advances in Differential Equations 2(1) (1997), 125-160.

[3] T. Faria and S. Trofimchuk, Nonmonotone travelling waves in a single species reaction-diffusion equation with delay, Journal of Differential Equations 228(1) (2006), 357-376.

DOI: https://doi.org/10.1016/j.jde.2006.05.006

[4] R. Huang, M. Mei, K. Zhang and Q. Zhang, Asymptotic stability of non-monotone traveling waves for time-delayed nonlocal dispersion equations, Discrete and Continuous Dynamical Systems 36(3) (2016), 1331-1353.

DOI: https://doi.org/10.3934/dcds.2016.36.1331

[5] S. A. Gourley and Y. Kuang, Wavefronts and global stability in a time-delayed population model with stage structure, Proceedings of the Royal Society of London: Series A 459(2034) (2003), 1563-1579.

DOI: https://doi.org/10.1098/rspa.2002.1094

[6] Y. Jiang and K. Zhang, Stability of traveling waves for nonlocal time-delayed reaction-diffusion equations, Kinetics and Related Models 5(11) (2018), 1235-1253.

DOI: https://doi.org/10.3934/krm.2018048

[7] C.-K. Lin and M. Mei, On traveling wavefronts of Nicholson’s blowflies equation with diffusion, Proceedings of the Royal Society of Edinburgh Section A: Mathematics 140(1) (2010), 135-152.

DOI: https://doi.org/10.1017/S0308210508000784

[8] C.-K. Lin, C.-T. Lin, Y. Lin and M. Mei, Exponential stability of nonmonotone traveling waves for Nicholson’s blowflies equation, SIAM Journal on Mathematical Analysis 46(2) (2014), 1053-1084.

DOI: https://doi.org/10.1137/120904391

[9] G. Y. Lv and M. X. Wang, Nonlinear stability of travelling wave fronts for delayed reaction diffusion equations, Nonlinearity 23(4) (2010), 845-873.

DOI: https://doi.org/10.1088/0951-7715/23/4/005

[10] M. Mei, C.-K. Lin, C.-T. Lin and J. W.-H. So, Traveling wavefronts for time-delayed reaction-diffusion equation: (I) local nonlinearity, Journal of Differential Equations 247(2) (2009), 495-510.

DOI: https://doi.org/10.1016/j.jde.2008.12.026

[11] M. Mei, C.-K. Lin, C.-T. Lin and J. W.-H. So, Traveling wavefronts for time-delayed reaction-diffusion equation: (II) Nonlocal nonlinearity, Journal of Differential Equations 247(2) (2009), 511-529.

DOI: https://doi.org/10.1016/j.jde.2008.12.020

[12] M. Mei and J. W.-H. So, Stability of strong travelling waves for a non-local time-delayed reaction-diffusion equation, Proceedings of the Royal Society of Edinburgh Section A: Mathematics 138(3) (2008), 551-568.

DOI: https://doi.org/10.1017/S0308210506000333

[13] M. Mei, J. W.-H. So, M. Y. Li and S. S. P. Shen, Asymptotic stability of travelling waves for Nicholson’s blowflies equation with diffusion, Proceedings of the Royal Society of Edinburgh Section A: Mathematics 134(3) (2004), 579-594.

DOI: https://doi.org/10.1017/S0308210500003358

[14] M. Mei, C. H. Ou and X. Q. Zhao, Global stability of monostable traveling waves for nonlocal time-delayed reaction-diffusion equations, SIAM Journal on Mathematical Analysis 42(6) (2010), 2762-2790.

DOI: https://doi.org/10.1137/090776342

[15] D. H. Sattinger, On the stability of waves of nonlinear parabolic systems, Advances in Mathematics 22(3) (1976), 312-355.

DOI: https://doi.org/10.1016/0001-8708(76)90098-0

[16] H. L. Smith and X. Q. Zhao, Global asymptotic stability of traveling waves in delayed reaction-diffusion equations, SIAM Journal on Mathematical Analysis 31(3) (2000), 514-534.

DOI: https://doi.org/10.1137/S0036141098346785

[17] X. H. Wang and G. Y. Lv, Global stability of travelling wave fronts for non-local diffusion-equations with delay, Izvestiya: Mathematics 78(2) (2014), 251-267.

DOI: https://doi.org/10.1070/IM2014v078n02ABEH002687

[18] Z. C. Wang, W. T. Li and S. G. Ruan, Traveling fronts in monostable equations with nonlocal delayed effects, Journal of Dynamics and Differential Equations 20(3) (2008), 573-607.

DOI: https://doi.org/10.1007/s10884-008-9103-8

[19] S. L. Wang, W. T. Li and S. Y. Liu, Oscillatory waves in reaction-diffusion equations with nonlocal delay and crossing-monostability, Nonlinear Analysis: Real World Applications 10(5) (2009), 3141-3151.

DOI: https://doi.org/10.1016/j.nonrwa.2008.10.012

[20] S. L. Wang and S. Y. Liu, Uniqueness of non-monotone traveling waves for delayed reaction-diffusion equations, Applied Mathematics Letters 22(7) (2009), 1056-1061.

DOI: https://doi.org/10.1016/j.aml.2009.01.014

[21] S. L. Wang, H. Q. Zhao and S. Y. Liu, Asymptotic stability of traveling waves for delayed reaction-diffusion equations with crossing-monostability, Zeitschrift für Angewandte Mathematik und Physik 62(3) (2011), 377-397.

DOI: https://doi.org/10.1007/s00033-010-0112-1

[22] Y. R. Yang, W. T. Li and S. L. Wang, Exponential stability of traveling fronts in a diffusion epidemic system with delay, Nonlinear Analysis: Real World Applications 12(2) (2011), 1223-1234.

DOI: https://doi.org/10.1016/j.nonrwa.2010.09.017

[23] G. B. Zhang, Global stability of traveling wave fronts for non-local delayed lattice differential equations, Nonlinear Analysis: Real World Applications 13(4) (2012), 1790-1801.

DOI: https://doi.org/10.1016/j.nonrwa.2011.12.010