Exponential attractors for two-dimensional nonlocal diffusion lattice systems with delay (original) (raw)

[1] M. Aouadi, Global and exponential attractors for extensible thermoelastic plate with time-varying delay, J. Differ. Equ., 269 (2020), 4079-4115. doi: 10.1016/j.jde.2020.03.026.
[2] P. W. Bates, P. C. Fife, X. Ren and X. Wang, Traveling waves in a convolution model for phase transitions, Arch. Ration. Mech. Anal., 138 (1997), 105-136. doi: 10.1007/s002050050037.
[3] T. Caraballo, F. Morillas and J. Valero, On differential equations with delay in Banach spaces and attractors for retarded lattice dynamical systems, Discret. Contin. Dyn. Syst., 34 (2014), 51-77. doi: 10.3934/dcds.2014.34.51.
[4] Z. Chen, B. Ermentrout and X. Wang, Wave propagation mediated by GABA B synapse and rebound excitation in an inhibitory network: a reduced model approach, J. Comput. Neuro., 5 (1998), 53-69.
[5] J. W. Cholewa and R. Czaja, Lattice dynamical systems: dissipative mechanism and fractal dimension of global and exponential attractors, J. Evol. Equ., 20 (2020), 485-515. doi: 10.1007/s00028-019-00535-3.
[6] C. Cortazar, M. Elgueta, J. D. Rossi and N. Wolanski, Boundary fluxes for nonlocal diffusion, J. Differ. Equ., 234 (2007), 360-390. doi: 10.1016/j.jde.2006.12.002.
[7] J. Coville and L. Dupaigne, On a non-local equation arising in population dynamics, Proc. Roy. Soc. Edinb. Sect. A, 137 (2007), 727-755. doi: 10.1017/S0308210504000721.
[8] F. Dong, W. Li and L. Zhang, Entire solutions in a two-dimensional nonlocal lattice dynamical system, Commun. Pure Appl. Anal., 17 (2018), 2517-2545. doi: 10.3934/cpaa.2018120.
[9] A. De Masi, T. Gobron and E. Presutti, Travelling fronts in non-local evolution equations, Arch. Ration. Mech. Anal., 132 (1995), 143-205. doi: 10.1007/BF00380506.
[10] A. Eden, C. Foias, B. Nicolaenko and R. Temam, Exponential attractors for dissipative evolution equations, Research in Applied Mathematics, vol. 37. Masson, Paris; John Wiley & Sons, Ltd., Chichester, 1994.
[11] M. Efendiev, A. Miranville and S. Zelik, Exponential attractors for a nonlinear reaction-diffusion system in mathbbR3\mathbb{R}^3 mathbbR3, C. R. Acad. Sci. Paris Sér. I Math., 330 (2000), 713-718. doi: 10.1016/S0764-4442(00)00259-7.
[12] M. Grasselli and D. Pra$\breve{z}$$\acute{a}$k, Exponential attractors for a class of reaction-diffusion problems with time delays, J. Evol. Equ., 7 (2007), 649-667. doi: 10.1007/s00028-007-0326-7.
[13] S. Habibi, Estimates on the dimension of an exponential attractor for a delay differential equation, Math. Slovaca, 64 (2014), 1237-1248. doi: 10.2478/s12175-014-0272-0.
[14] M. A. Hammami, L. Mchiri, S. Netchaoui and S. Sonner, Pullback exponential attractors for differential equations with variable delays, Discrete Contin. Dyn. Syst. Ser. B, 25 (2020), 301-319. doi: 10.3934/dcdsb.2019183.
[15] X. Han, Exponential attractors for lattice dynamical systems in weighted spaces, Discrete Contin. Dyn. Syst., 31 (2011), 445-467. doi: 10.3934/dcds.2011.31.445.
[16] X. Han and P. E. Kloeden, Asymptotic behavior of a neural field lattice model with a Heaviside operator, Phys. D, 389 (2019), 1-12. doi: 10.1016/j.physd.2018.09.004.
[17] L. I. Ignat and J. D. Rossi, A nonlocal convection-diffusion equation, J. Funct. Anal., 251 (2007), 399-437. doi: 10.1016/j.jfa.2007.07.013.
[18] C. T. Lee, et al., Non-local Concepts and Models in Biology, J. Theory Biol., 210 (2001), 201-219.
[19] S. Ma, P. Weng and X. Zou, Asymptotic speed of propagation and traveling wavefronts in a non-local delayed lattice differential equation, Nonlinear Anal., 65 (2006), 1858-1890. doi: 10.1016/j.na.2005.10.042.
[20] J. D. Murray, Mathematical Biology, Springer-Verlag, Berlin, 1989. doi: 10.1007/978-1-4612-0873-0. doi: 10.1007/978-1-4612-0873-0.
[21] E. Orlandi and L. Triolo, Travelling fronts in nonlocal models for phase separation in an external field, Proc. Roy. Soc. Edinb. Sect. A, 127 (1997), 823-835. doi: 10.1017/S0308210500023854.
[22] D. Pra$\breve{z}$$\acute{a}$k, Exponential attractors for abstract parabolic systems with bounded delay, Bull. Austral. Math. Soc., 76 (2007), 285-295. doi: 10.1017/S0004972700039666.
[23] Z. Wang, W. Li and J. Wu, Entire solutions in delayed lattice differential equations with monostable nonlinearity, SIAM J. Math. Anal., 40 (2009), 2392-2420. doi: 10.1137/080727312.
[24] A. Yagi, Abstract Parabolic Evolution Equations and their Applications, Springer-Verlag, Berlin, 2010.
[25] G. Zhang, Global stability of traveling wave fronts for non-local delayed lattice differential equations, Nonlinear Anal. Real World Appl., 13 (2012), 1790-1801. doi: 10.1016/j.nonrwa.2011.12.010.
[26] S. Zhou and W. Shi, Attractors and dimension of dissipative lattice systems, J. Differ. Equ., 224 (2006), 172-204. doi: 10.1016/j.jde.2005.06.024.