Citation: |
[1] |
M. Aguerra, C. Gomez and S. Trofimchuk, On uniqueness of semi-wavefronts, Math. Ann., 354 (2012), 73-109.doi: 10.1007/s00208-011-0722-8. |
[2] |
F. Andreu-Vaillo, J. M. Mazon, J. D. Rossi and J. J. Toledo-Melero, Nonlocal Diffusion Problems, Math. Surveys and Monographs, Vol. 165, Amer. Math. Soc., 2010.doi: 10.1090/surv/165. |
[3] |
E. Chasseigne, M. Chaves and J. Rossi, Asymptotic behavior for nonlocal diffusion equations, J. Math. Pure Appl., 86 (2006), 271-291.doi: 10.1016/j.matpur.2006.04.005. |
[4] |
C. Cortazar, M. Elgueta, J. D. Rossi and N. Wolanski, How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems, Arch. Rational Mech. Anal., 187 (2008), 137-156.doi: 10.1007/s00205-007-0062-8. |
[5] |
J. Coville, On uniqueness and monotonicity of solutions of non-local reaction-diffusion equation, Annali. di Matematica Pura Appl., 185 (2006), 461-485.doi: 10.1007/s10231-005-0163-7. |
[6] |
J. Coville, J. Dávila and S. Martínez, Nonlocal anisotropic dispersal with monostable nonlinearity, J. Differential Equations, 244 (2008), 3080-3118.doi: 10.1016/j.jde.2007.11.002. |
[7] |
J. Coville and L. Dupaigne, On a non-local equation arising in population dynamics, Proc. Roy. Soc. Edinburgh Sect. A, 137 (2007), 727-755.doi: 10.1017/S0308210504000721. |
[8] |
J. Coville and L. Dupaigne, Propagation speed of travelling fronts in non local reaction-diffusion equations, Nonlinear Anal., 60 (2005), 797-819.doi: 10.1016/j.na.2003.10.030. |
[9] |
J. Fang and X.-Q. Zhao, Existence and uniqueness of traveling waves for non-monotone integral equations with applications, J. Differential Equations, 248 (2010), 2199-2226.doi: 10.1016/j.jde.2010.01.009. |
[10] |
P. C. Fife, Mathematical Aspects of Reacting and Diffusing Systems, Lecture Notes in Biomathematics, 28, Springer-Verlag, Berlin-New York, 1979. |
[11] |
W. S. C. Gurney, S. P. Blythe and R. M. Nisbet, Nicholson's blowflies revisited, Nature, 287 (1980), 17-21.doi: 10.1038/287017a0. |
[12] |
A. Gomez and S. Trofimchuk, Global continuation of monotone wavefronts, J. London Math. Soc., 89 (2014), 47-68.doi: 10.1112/jlms/jdt050. |
[13] |
S. A. Gourley, J. W.-H. So and J. Wu, Nonlocalily of reaction-diffusion equations induced by delay: Biological modeling and nonlinear dynamics, (Russian) Sovrem. Mat. Fundam. Napravl., 1 (2003), 84-120; translation in J. Math. Sci., 124 (2004), 5119-5153.doi: 10.1023/B:JOTH.0000047249.39572.6d. |
[14] |
S. A. Gourley and J. Wu, Delayed non-local diffusive systems in biological invasion and disease spread, in Nonlinear Dynamics and Evolution Equations (eds. H. Brunner, X.-Q. Zhao and X. Zou), Fields Institute Communications, 48, Amer. Math. Soc., Providence, RI, 2006, 137-200. |
[15] |
R. Huang, M. Mei and Y. Wang, Planar traveling waves for nonlocal dispersion equation with monostable nonlinearity, Discret. Contin. Dyn. Syst. A, 32 (2012), 3621-3649.doi: 10.3934/dcds.2012.32.3621. |
[16] |
L. Ignat and J. D. Rossi, Decay estimates for nonlocal problems via energy methods, J. Math. Pure Appl.(9), 92 (2009), 163-187.doi: 10.1016/j.matpur.2009.04.009. |
[17] |
L. Ignat and J. D. Rossi, A nonlocal convolution-diffusion equation, J. Func. Anal., 251 (2007), 399-437.doi: 10.1016/j.jfa.2007.07.013. |
[18] |
D. Liang and J. Wu, Travelling waves and numerical approximations in a reaction advection diffusion equation with nonlocal delayed effects, J. Nonlinear Sci., 13 (2003), 289-310.doi: 10.1007/s00332-003-0524-6. |
[19] |
C.-K. Lin, C.-T. Lin, Y. P. Lin and M. Mei, Exponential stability of nonmonotone traveling waves for Nicholson's blowflies equation, SIAM J. Math. Anal., 46 (2014), 1053-1084.doi: 10.1137/120904391. |
[20] |
M. C. Mackey and L. Glass, Oscillation and chaos in physiological control systems, Science, 197 (1977), 287-289.doi: 10.1126/science.267326. |
[21] |
A. Matsumura and M. Mei, Nonlinear stability of viscous shock profile for a non-convex system of viscoelasticity, Osaka J. Math., 34 (1997), 589-603. |
[22] |
M. Mei, C.-K. Lin, C.-T. Lin and J. W.-H. So, Traveling wavefronts for time-delayed reaction-diffusion equation. I. Local nonlinearity, J. Differential Equations, 247 (2009), 495-510.doi: 10.1016/j.jde.2008.12.026. |
[23] |
M. Mei, C.-K. Lin, C.-T. Lin and J. W.-H. So, Traveling wavefronts for time-delayed reaction-diffusion equation. II. Nonlocal nonlinearity, J. Differential Equations, 247 (2009), 511-529.doi: 10.1016/j.jde.2008.12.020. |
[24] |
M. Mei, J. W.-H. So, M. Li and S. Shen, Asymptotic stability of travelling waves for Nicholson's blowflies equation with diffusion, Proc. Roy. Soc. Edinburgh Sec. A, 134 (2004), 579-594.doi: 10.1017/S0308210500003358. |
[25] |
M. Mei and J. W.-H. So, Stability of strong travelling waves for a non-local time-delayed reaction-diffusion equation, Proc. Roy. Soc. Edinburgh Sec. A, 138 (2008), 551-568.doi: 10.1017/S0308210506000333. |
[26] |
M. Mei, C. Ou and X.-Q. Zhao, Global stability of monostable traveling waves for nonlocal time-delayed reaction-diffusion equations, SIAM J. Math. Anal., 42 (2010), 2762-2790; Erratum, SIAM J. Math. Anal., 44 (2012), 538-540.doi: 10.1137/090776342. |
[27] |
M. Mei and Y. Wang, Remark on stability of traveling waves for nonlocal Fisher-KPP equations, Int. J. Numer. Anal. Model. Seris B, 2 (2011), 379-401. |
[28] |
M. Mei and Y. S. Wong, Novel stability results for traveling wavefronts in an age-structured reaction-diffusion equations, Math. Biosci. Engin., 6 (2009), 743-752.doi: 10.3934/mbe.2009.6.743. |
[29] |
J. A. J. Metz and O. Diekmann, The dynamics of Physiologically Structured Populations, Springer, New York, 1986.doi: 10.1007/978-3-662-13159-6. |
[30] |
H. J. K. Moet, A note on the asymptotic behavior of solutions of the KPP equation, SIAM J. Math. Anal., 10 (1979), 728-732.doi: 10.1137/0510067. |
[31] |
S. Pan, W.-T. Li and G. Lin, Existence and stability of traveling wavefronts in a nonlocal diffusion equation with delay, Nonlinear Anal., 72 (2010), 3150-3158.doi: 10.1016/j.na.2009.12.008. |
[32] |
J. W.-H. So, J. Wu and X. Zou, A reaction-diffusion model for a single species with age structure: I. Traveling wavefronts on unbounded domains, Roy. Soc. London Proc. Series A Math. Phys. Eng. Sci., 457 (2001), 1841-1853.doi: 10.1098/rspa.2001.0789. |
[33] |
E. Trofimchuk and S. Trofimchunk, Admissible wavefront speeds for a single species reaction-diffusion equation with delay, Discrete Contin. Dyn. Syst. A, 20 (2008), 407-423.doi: 10.3934/dcds.2008.20.407. |
[34] |
E. Trofimchuk, V. Tkachenko and S. Trofimchuk, Slowly oscillating wave solutions of a single species reaction-diffusion equation with delay, J. Differential Equations, 245 (2008), 2307-2332.doi: 10.1016/j.jde.2008.06.023. |
[35] |
S.-L. Wu, H.-Q. Zhao and S.-Y. Liu, Asymptotic stability of traveling waves for delayed reaction-diffusion equations with crossing-monostability, Z. Angew. Math. Phys., 62 (2011), 377-397.doi: 10.1007/s00033-010-0112-1. |
[36] |
H. Yagisita, Existence and nonexistence of traveling waves for a nonlocal monostable equation, Publ. Res. Inst. Math. Sci., 45 (2009), 925-953.doi: 10.2977/prims/1260476648. |
[37] |
G.-B. Zhang, Traveling waves in a nonlocal dispersal population model with age-structure, Nonlinear Anal., 74 (2011), 5030-5047.doi: 10.1016/j.na.2011.04.069. |
[38] |
G.-B. Zhang and R. Ma, Spreading speeds and traveling waves for a nonlocal dispersal equation with convolution-type crossing-monostable nonlinearity, Z. Ang. Math. Phys., 64 (2013), 1643-1659.doi: 10.1007/s00033-013-0353-x. |