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Monotonicity, asymptotics and uniqueness of travelling wave solution of a non-local delayed lattice dynamical system
1. | Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, China |
2. | College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China |
References:
[1] |
M. Aguerrea, C. Gomez and S. Trofimchuk, On uniqueness of semi-wavefronts: Diekmann-Kaper theory of a nonlinear convolution equation re-visited, Math. Ann., 354 (2012), 73-109.
doi: 10.1007/s00208-011-0722-8. |
[2] |
P. W. Bates and A. Chmaj, A discrete convolution model for phase transition, Arch. Ration. Mech. Anal., 150 (1999), 281-305.
doi: 10.1007/s002050050189. |
[3] |
H. Berestycki and L. Nirenberg, On the method of moving planes and the sliding method, Bol. Soc. Brasil. Math., 22 (1991), 1-37.
doi: 10.1007/BF01244896. |
[4] |
X. Chen and J.-S. Guo, Uniqueness and existence of traveling waves for discrete quasilinear monostable dynamics, Math. Ann., 326 (2003), 123-146.
doi: 10.1007/s00208-003-0414-0. |
[5] |
X. Chen, S.-C. Fu and J.-S. Guo, Uniqueness and asymptotics of traveling waves of monostable dynamics on lattices, SIAM J. Math. Anal., 38 (2006), 233-258.
doi: 10.1137/050627824. |
[6] |
X. Chen and J.-S. Guo, Existence and asymptotic stability of traveling waves of discrete quasilinear monostable equations, J. Differential Equations, 184 (2002), 549-569.
doi: 10.1006/jdeq.2001.4153. |
[7] |
J. Coville, On uniqueness and monotonicity of non-local reaction diffusion equation, Ann. Mat. Pura Appl., 185 (2006), 461-485.
doi: 10.1007/s10231-005-0163-7. |
[8] |
S.-N. Chow, J. Mallet-Paret and W. X. Shen, Travelling waves in lattice dynamical systems, J. Differential Equations, 149 (1998), 248-291.
doi: 10.1006/jdeq.1998.3478. |
[9] |
J. Carr and A. Chmaj, Uniqueness of travelling waves for nonlocal monostable equations, Proc. Amer. Math. Soc., 132 (2004), 2433-2439.
doi: 10.1090/S0002-9939-04-07432-5. |
[10] |
O. Diekmann and H. Kaper, On the bounded solutions of a nonlinear convolution equation, Nonlinear Anal. TMA., 2 (1978), 721-737.
doi: 10.1016/0362-546X(78)90015-9. |
[11] |
J. Fang, J. Wei and X.-Q. Zhao, Uniqueness of traveling waves for nonlocal lattice equations, Proc. Amer. Math. Soc., 139 (2010), 1361-1373.
doi: 10.1090/S0002-9939-2010-10540-3. |
[12] |
J. Fang, J. Wei and X.-Q. Zhao, Spreading speed and travelling waves for non-monotone time-delayed lattice equations, Proc. Roy. Math. Soc. Lond. A., 466 (2010), 1919-1934.
doi: 10.1098/rspa.2009.0577. |
[13] |
J.-S. Guo and Y.-C. Lin, Traveling wave solution for a lattice dynamical system with convolution type nonlinearity, Discrete Contin. Dyn. Syst., 32 (2012), 101-124.
doi: 10.3934/dcds.2012.32.101. |
[14] |
X. Liang and X.-Q. Zhao, Asymptotic speeds of spread and traveling waves for monotone semiflows with application, Comm. Pure Appl. Math., 60 (2007), 1-40.
doi: 10.1002/cpa.20154. |
[15] |
S. W. Ma and X. F. Zou, Existence, uniqueness and stability of travelling waves in a discrete reaction-diffusion monostable equation with delay, J. Differential Equations, 217 (2005), 54-87.
doi: 10.1016/j.jde.2005.05.004. |
[16] |
S. W. Ma, P. X. Weng and X. F. Zou, Asymptotic speed of propagation and traveling wavefronts in a non-local delayed lattice differential equation, Nonlinear Analysis, 65 (2006), 1858-1890.
doi: 10.1016/j.na.2005.10.042. |
[17] |
H. R. Thieme and X.-Q. Zhao, Asymptotic speeds of spred and traveling waves for integral equations and delayed reaction-diffusion models, J. Differential Equations, 195 (2003), 430-470.
doi: 10.1016/S0022-0396(03)00175-X. |
[18] |
D. V. Widder, The Laplace Transform, Princeton University Press, Princeton, NJ, 1941. |
[19] |
P. X. Weng, H. X. Huang and J. H. Wu, Asymptotic speed of propagation of wave fronts in a lattice delay differential equation with global interaction, IMA J. Appl. Math., 68 (2003), 409-439.
doi: 10.1093/imamat/68.4.409. |
[20] |
J. H. Wu and X. F. Zou, Asymptotic and periodic boundary value problems of mixed FDEs and wave solutions of lattice differential equations, J. Differential Equations, 135 (1997), 315-357.
doi: 10.1006/jdeq.1996.3232. |
[21] |
Z. X. Yu, Uniqueness of critical traveling waves for nonlocal lattice equations with delays, Proc. Amer. Math. Soc., 140 (2012), 3853-3859.
doi: 10.1090/S0002-9939-2012-11225-0. |
[22] |
P. A. Zhang and W. T. Li, Moonotonicity and uniqueness of traveling waves for a reaction-diffusion model with a quiescent stage, Nonlinear Anal. TMA., 72 (2010), 2178-2189.
doi: 10.1016/j.na.2009.10.016. |
[23] |
B. Zinner, G. Harris and W. Hudson, Traveling wavefronts for the discrete Fisher's equation, J. Differential Equations, 105 (1993), 46-62.
doi: 10.1006/jdeq.1993.1082. |
show all references
References:
[1] |
M. Aguerrea, C. Gomez and S. Trofimchuk, On uniqueness of semi-wavefronts: Diekmann-Kaper theory of a nonlinear convolution equation re-visited, Math. Ann., 354 (2012), 73-109.
doi: 10.1007/s00208-011-0722-8. |
[2] |
P. W. Bates and A. Chmaj, A discrete convolution model for phase transition, Arch. Ration. Mech. Anal., 150 (1999), 281-305.
doi: 10.1007/s002050050189. |
[3] |
H. Berestycki and L. Nirenberg, On the method of moving planes and the sliding method, Bol. Soc. Brasil. Math., 22 (1991), 1-37.
doi: 10.1007/BF01244896. |
[4] |
X. Chen and J.-S. Guo, Uniqueness and existence of traveling waves for discrete quasilinear monostable dynamics, Math. Ann., 326 (2003), 123-146.
doi: 10.1007/s00208-003-0414-0. |
[5] |
X. Chen, S.-C. Fu and J.-S. Guo, Uniqueness and asymptotics of traveling waves of monostable dynamics on lattices, SIAM J. Math. Anal., 38 (2006), 233-258.
doi: 10.1137/050627824. |
[6] |
X. Chen and J.-S. Guo, Existence and asymptotic stability of traveling waves of discrete quasilinear monostable equations, J. Differential Equations, 184 (2002), 549-569.
doi: 10.1006/jdeq.2001.4153. |
[7] |
J. Coville, On uniqueness and monotonicity of non-local reaction diffusion equation, Ann. Mat. Pura Appl., 185 (2006), 461-485.
doi: 10.1007/s10231-005-0163-7. |
[8] |
S.-N. Chow, J. Mallet-Paret and W. X. Shen, Travelling waves in lattice dynamical systems, J. Differential Equations, 149 (1998), 248-291.
doi: 10.1006/jdeq.1998.3478. |
[9] |
J. Carr and A. Chmaj, Uniqueness of travelling waves for nonlocal monostable equations, Proc. Amer. Math. Soc., 132 (2004), 2433-2439.
doi: 10.1090/S0002-9939-04-07432-5. |
[10] |
O. Diekmann and H. Kaper, On the bounded solutions of a nonlinear convolution equation, Nonlinear Anal. TMA., 2 (1978), 721-737.
doi: 10.1016/0362-546X(78)90015-9. |
[11] |
J. Fang, J. Wei and X.-Q. Zhao, Uniqueness of traveling waves for nonlocal lattice equations, Proc. Amer. Math. Soc., 139 (2010), 1361-1373.
doi: 10.1090/S0002-9939-2010-10540-3. |
[12] |
J. Fang, J. Wei and X.-Q. Zhao, Spreading speed and travelling waves for non-monotone time-delayed lattice equations, Proc. Roy. Math. Soc. Lond. A., 466 (2010), 1919-1934.
doi: 10.1098/rspa.2009.0577. |
[13] |
J.-S. Guo and Y.-C. Lin, Traveling wave solution for a lattice dynamical system with convolution type nonlinearity, Discrete Contin. Dyn. Syst., 32 (2012), 101-124.
doi: 10.3934/dcds.2012.32.101. |
[14] |
X. Liang and X.-Q. Zhao, Asymptotic speeds of spread and traveling waves for monotone semiflows with application, Comm. Pure Appl. Math., 60 (2007), 1-40.
doi: 10.1002/cpa.20154. |
[15] |
S. W. Ma and X. F. Zou, Existence, uniqueness and stability of travelling waves in a discrete reaction-diffusion monostable equation with delay, J. Differential Equations, 217 (2005), 54-87.
doi: 10.1016/j.jde.2005.05.004. |
[16] |
S. W. Ma, P. X. Weng and X. F. Zou, Asymptotic speed of propagation and traveling wavefronts in a non-local delayed lattice differential equation, Nonlinear Analysis, 65 (2006), 1858-1890.
doi: 10.1016/j.na.2005.10.042. |
[17] |
H. R. Thieme and X.-Q. Zhao, Asymptotic speeds of spred and traveling waves for integral equations and delayed reaction-diffusion models, J. Differential Equations, 195 (2003), 430-470.
doi: 10.1016/S0022-0396(03)00175-X. |
[18] |
D. V. Widder, The Laplace Transform, Princeton University Press, Princeton, NJ, 1941. |
[19] |
P. X. Weng, H. X. Huang and J. H. Wu, Asymptotic speed of propagation of wave fronts in a lattice delay differential equation with global interaction, IMA J. Appl. Math., 68 (2003), 409-439.
doi: 10.1093/imamat/68.4.409. |
[20] |
J. H. Wu and X. F. Zou, Asymptotic and periodic boundary value problems of mixed FDEs and wave solutions of lattice differential equations, J. Differential Equations, 135 (1997), 315-357.
doi: 10.1006/jdeq.1996.3232. |
[21] |
Z. X. Yu, Uniqueness of critical traveling waves for nonlocal lattice equations with delays, Proc. Amer. Math. Soc., 140 (2012), 3853-3859.
doi: 10.1090/S0002-9939-2012-11225-0. |
[22] |
P. A. Zhang and W. T. Li, Moonotonicity and uniqueness of traveling waves for a reaction-diffusion model with a quiescent stage, Nonlinear Anal. TMA., 72 (2010), 2178-2189.
doi: 10.1016/j.na.2009.10.016. |
[23] |
B. Zinner, G. Harris and W. Hudson, Traveling wavefronts for the discrete Fisher's equation, J. Differential Equations, 105 (1993), 46-62.
doi: 10.1006/jdeq.1993.1082. |
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