×

zbMATH — the first resource for mathematics

Compact kernel sections for lattice systems with delays. (English) Zbl 1169.34055
The authors consider a process associated to a non-autonomous lattice system with delay, and prove the existence, upper semi-continuity and singular limiting behavior of compact kernel sections.

MSC:
34K30 Functional-differential equations in abstract spaces
35R10 Partial functional-differential equations
34K25 Asymptotic theory of functional-differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bates, P.W.; Lu, K.; Wang, B., Attractors for lattice dynamical systems, Internat. J. bifurc. chaos, 11, 1, 143-153, (2001) · Zbl 1091.37515
[2] Bates, P.W.; Chen, X.; Chmaj, A., Traveling waves of bistable dynamics on a lattice, SIAM J. math. anal., 35, 520-546, (2003) · Zbl 1050.37041
[3] Bates, P.W.; Lisei, H.; Lu, K., Attractors for stochastic lattice dynamical systems, Stoch. dyn., 6, 1-21, (2006) · Zbl 1105.60041
[4] Beyn, W.-J.; Yu Pilyugin, S., Attractors of reaction-diffusion systems on infinite lattices, J. differential equations, 15, 485-515, (2003) · Zbl 1041.37040
[5] Caraballo, T.; Real, J., Navier – stokes equations with delays, Roy. soc. London proc. ser. A. math. phys. eng. sci., 457, 2441-2453, (2001) · Zbl 1007.35062
[6] Caraballo, T.; Real, J., Asymptotic behavior of navier – stokes equations with delays, Roy. soc. London proc. ser. A. math. phys. eng. sci., 459, 3181-3194, (2003) · Zbl 1057.35027
[7] Caraballo, T.; Real, J., Attractors for 2D-navier – stokes models with delays, J. differential equations, 205, 271-297, (2004) · Zbl 1068.35088
[8] Caraballo, T.; Marín-Rubio, P.; Valero, J., Autonomous and non-autonomous attractors for differential equations with delays, J. differential equations, 208, 9-41, (2005) · Zbl 1074.34070
[9] Chepyzhov, V.V.; Vishik, M.I., Attractors for equations of mathematical physics, (2002), American Mathematical Society, Colloquium Publications, p. 49 · Zbl 0986.35001
[10] Chow, S.N., Lattice dynamical systems, Lect. notes. math., 1822, 1-102, (2003) · Zbl 1046.37051
[11] Fan, X.M.; Wang, Y.G., Attractors for a second order nonautonomous lattice dynamical system with nonlinear damping, Phys. lett. A, 365, 17-27, (2007) · Zbl 1203.37122
[12] Hale, J.K., Theory of functional differential equations, (1977), Springer Berlin · Zbl 0425.34048
[13] Hale, J.K., Asymptotic behavior of dissipative systems, (1988), AMS Providence, RI, p. 25 · Zbl 0642.58013
[14] Hale, J.K.; Verduyn Lunel, S.M., Introduction to functional differential equations, (1993), Springer-Verlag New York · Zbl 0787.34002
[15] Karachalios, N.I.; Yannacopoulos, A.N., Global existence and compact attractors for the discrete nonlinear Schrödinger equation, J. differential equations, 217, 88-123, (2005) · Zbl 1084.35092
[16] Kuang, Y., Delay differential equations with applications in population dynamics, (1993), Academic Press Boston · Zbl 0777.34002
[17] Ma, Q.; Wang, S.; Zhong, C., Necessary and sufficient conditions for the existence of global attractors for semigroup and application, Indiana univ. math. J., 51, 6, 1541-1559, (2002) · Zbl 1028.37047
[18] Mallet-Paret, J.; Sell, G., Systems of differential delay equations: Floquet multipliers and discrete Lyapunov functions, J. differential equations, 125, 2, 385-440, (1996) · Zbl 0849.34055
[19] Mallet-Paret, J.; Sell, G.R., The poincaré-bendixson theorem for monotone cyclic feedback systems with delay, J. differential equations, 125, 2, 441-489, (1996) · Zbl 0849.34056
[20] Rezounenko, A.V.; Wu, J., A non-local PDE model for population dynamics with state-selective delay: local theory and global attractors, J. comput. appl. math., 190, 99-113, (2006) · Zbl 1082.92039
[21] Rezounenko, A.V., Partial differential equations with discrete and distributed state-dependent delays, J. math. anal. appl., 326, 1031-1045, (2007) · Zbl 1178.35370
[22] Van Vleck, E.; Wang, B., Attractors for lattice fitzhugh – nagumo systems, Physica D, 212, 317-336, (2005) · Zbl 1086.34047
[23] Wu, J., ()
[24] Wang, B., Attractors for reaction diffusion equations in unbounded domains, Physica D, 128, 41-52, (1999) · Zbl 0953.35022
[25] Wang, B., Dynamics of systems on infinite lattices, J. differential equations, 221, 224-245, (2006) · Zbl 1085.37056
[26] Wang, B., Asymptotic behavior of non-autonomous lattice systems, J. math. anal. appl., 331, 121-136, (2007) · Zbl 1112.37076
[27] Zhao, C.; Zhou, S., Compact kernel sections for non-autonomous klein – gordon – schrödinger equations on infinite lattices, J. math. anal. appl., 332, 32-56, (2007) · Zbl 1113.37057
[28] Zhao, X.; Zhou, S., Kernel sections for processes and nonautonomous lattice systems, Discrete. contin. dyn. syst. (series B), 9, 763-785, (2008) · Zbl 1149.37040
[29] Zhou, S., Attractors for second order lattice dynamical systems, J. differential equations, 179, 605-624, (2002) · Zbl 1002.37040
[30] Zhou, S., Attractors for first order dissipative lattice dynamical systems, Physica D, 178, 51-61, (2003) · Zbl 1011.37047
[31] Zhou, S., Attractors and approximations for lattice dynamical systems, J. differential equations, 200, 342-368, (2004) · Zbl 1173.37331
[32] Zhou, S.; Shi, W., Attractors and dimension of dissipative lattice systems, J. differential equations, 224, 172-204, (2006) · Zbl 1091.37023
[33] Zhou, S.; Zhao, C.; Liao, X., Compact uniform attractors for dissipative non-autonomous lattice dynamical systems, Commun. pure appl. anal., 6, 1087-1111, (2007) · Zbl 1136.37043
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.