`a`
Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Traveling wave solution for a lattice dynamical system with convolution type nonlinearity
Pages: 101 - 124, Issue 1, January 2012

doi:10.3934/dcds.2012.32.101      Abstract        References        Full text (412.9K)           Related Articles

Jong-Shenq Guo - Department of Mathematics, Tamkang University, 151, Ying-Chuan Road, Tamsui, Taipei County 25137, Taiwan (email)
Ying-Chih Lin - Department of Mathematics, National Taiwan Normal University, 88, S-4, Ting Chou Road, Taipei 11677, Taiwan (email)

1 P. W. Bates, P. C. Fife, X. Ren and X. Wang, Traveling waves in a convolution model for phase transitions, Arch. Rational Mech. Anal., 138 (1997), 105-136.       
2 P. W. Bates, X. Chen and A. Chmaj, Traveling waves of bistable dynamics on a lattice, SIAM J. Math. Anal., 35 (2003), 520-546.       
3 J. Carr and A. Chmaj, Uniqueness of travelling waves for nonlocal monostable equations, Proc. Amer. Math. Soc., 132 (2004), 2433-2439.       
4 X. Chen, Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations, Advances in Differential Equations, 2 (1997), 125-160.       
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.       
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.       
7 X. Chen and J.-S. Guo, Uniqueness and existence of traveling waves for discrete quasilinear monostable dynamics, Math. Ann., 326 (2003), 123-146.       
8 J. Coville and L. Dupaigne, Travelling fronts in integrodifferential equations, C. R. Math. Acad. Sci. Paris, 337 (2003), 25-30.       
9 J. Coville and L. Dupaigne, Propagation speed of travelling fronts in non local reaction-diffusion equations, Nonlinear Anal., 60 (2005), 797-819.       
10 J. Coville and L. Dupaigne, On a non-local equation arising in population dynamics, Proc. Roy. Soc. Edinburgh Sect. A, 137 (2007), 727-755.       
11 S.-C. Fu, J.-S. Guo and S.-Y. Shieh, Traveling wave solutions for some discrete quasilinear parabolic equations, Nonlinear Analysis Series A, 48 (2002), 1137-1149.       
12 W. Hudson and B. Zinner, Existence of traveling waves for reaction diffusion equations of Fisher type in periodic media, World Sci. Publ., 1 (1995), 187-199.       
13 G. Lv, Asymptotic behavior of traveling fronts and entire solutions for a nonlinear monostable equation, Nonlinear Analysis, 72 (2010), 3659-3668.       
14 S. Ma and X. Zou, Existence, uniqueness and stability of traveling waves in a discrete reaction-diffusion monostable equation with delay, J. Differential Equations, 217 (2005), 54-87.       
15 S. Ma and X. Zou, Propagation and its failure in a lattice delayed differential equation with global interaction, J. Differential Equations, 212 (2005), 129-190.       
16 S. Ma, P. Weng and X. Zou, Asymptotic speed of propagation and traveling wavefronts in a non-local delayed lattice differential equation, Nonlinear Analysis, 65 (2006), 1858-1890.       
17 K. Schumacher, Travelling-front solutions for integro-differential equations, J. Reine Angew. Math., 316 (1980), 54-70.       
18 P. Weng, H. Huang and J. 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.       
19 B. Zinner, Stability of traveling wavefronts for the discrete Nagumo equation, SIAM J. Math. Anal., 22 (1991), 1016-1020.       
20 B. Zinner, Existence of traveling wavefront solutions for the discrete Nagumo equation, J. Differential Equations, 96 (1992), 1-27.       
21 B. Zinner, G. Harris and W. Hudson, Traveling wavefronts for the discrete Fisher's equation, J. Differential Equations, 105 (1993), 46-62.       

Go to top