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Tytuł artykułu

Attractors for non-autonomous retarded lattice dynamical systems

Treść / Zawartość

Warianty tytułu

Języki publikacji

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Abstrakty

EN
In this paperwe study a non-autonomous lattice dynamical system with delay. Under rather general growth and dissipative conditions on the nonlinear term,we define a non-autonomous dynamical system and prove the existence of a pullback attractor for such system as well. Both multivalued and single-valued cases are considered.

Wydawca

Rocznik

Tom

2

Numer

1

Opis fizyczny

Daty

online
2015-06-16

Twórcy

  • Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080- Sevilla, Spain
  • Department d’Economia Aplicada, Facultat d’Economia, Universitat de Valéncia, Campus del Tarongers s/n, 46022-Valéncia, Spain
autor
  • Centro de Investigación Operativa, Universidad Miguel Hernández, Avda. de la Universidad, s/n, 03202-Elche, Spain

Bibliografia

  • [1] A.Y. Abdallah, Exponential attractors for first-order lattice dynamical systems, J. Math. Anal. Appl., 339 (2008), 217-224.
  • [2] J.M. Amigó, A. Giménez, F. Morillas and J. Valero, Attractors for a lattice dynamical system generated by non-newtonian fluids modeling suspensions, Internat. J. Bifur. Chaos, 20 (2010), 2681-2700. [WoS]
  • [3] V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Editura Academiei, Bucuresti, 1976.
  • [4] P.W. Bates, H. Lisei and K. Lu, Attractors for stochastic lattice dynamical systems, Stochastics & Dynamics, 6 (2006), no.1, 1–21.
  • [5] P.W. Bates, K. Lu and B. Wang, Attractors for lattice dynamical systems, Internat. J. Bifur. Chaos, 11 (2001), 143–153.
  • [6] T. Caraballo, M.J. Garrido-Atienza, B. Schmalfuß and J. Valero, Non-autonomous and random attractors for delay random semilinear equations without uniqueness, Discrete Contin. Dyn. Syst., 21 (2008), 415-443.
  • [7] T. Caraballo and P. E. Kloeden, Non-autonomous attractors for integro-differential evolution equations, Discrete and Continuous Dynamical Systems Series S. , 2 (2009), 17-36.
  • [8] T. Caraballo and K. Lu, Attractors for stochastic lattice dynamical systems with a multiplicative noise, Front. Math. China, 3 (2008), 317-335. [WoS][Crossref]
  • [9] T. Caraballo, T. Lukaszewicz and J. Real, Pullback attractors for non-autonomous 2D-Navier-Stokes equations in some unbounded domains, C. R. Acad. Sci. Paris, Ser. I, 342 (2006), 263-268.
  • [10] T. Caraballo, T. Lukaszewicz and J. Real, Pullback attractors for asymptotically compact nonautonomous dynamical systems, Nonlinear Anal., 64 (2006), 484-498.
  • [11] T. Caraballo, F. Morillas and J. Valero, Random Attractors for stochastic lattice systems with non-Lipschitz nonlinearity, J. Diff. Equat. App., 17 (2011), no2, 161-184. [Crossref]
  • [12] T. Caraballo, F. Morillas and J. Valero, Attractors of stochastic lattice dynamical systems with a multiplicative noise and non-Lipschitz nonlinearities, J. Differential Equations, 253 (2012), no. 2, 667-693. [WoS]
  • [13] T. Caraballo, F. Morillas and J. Valero, On differential equations with delay in Banach spaces and attractors for retarded lattice dynamical systems, Discrete Cont. Dyn. Systems, Series A, 34 (2014), 51-77.
  • [14] A.M. Gomaa, On existence of solutions and solution sets of differential equations and differential inclusions with delay in Banach spaces, J. Egyptian Math. Soc. (2012, to appear).
  • [15] X. Han, Random attractors for stochastic sine-Gordon lattice systems with multiplicative white noise, J. Math. Anal. Appl., 376 (2011), 481-493. [WoS]
  • [16] X. Han, W. Shen, S. Zhou, Random attractors for stochastic lattice dynamical systems in weighted spaces, J. Differential Equations, 250 (2011), 1235-1266.
  • [17] V. Lakshmikantham, A.R. Mitchell, R.W. Mitchell, On the existence of solutions of differential equations of retarde type in a Banach space, Annales Polonici Mathematici, XXXV (1978), 253-260.
  • [18] P.Marín-Rubio, J. Real, On the relation between two different concepts of pullback attractors for non-autonomous dynamical systems, Nonlinear Anal., 71 (2009), 3956-3963.
  • [19] F. Morillas, J. Valero, A Peano’s theorem and attractors for lattice dynamical systems, Internat. J. Bifur. Chaos, 19 (2009), 557-578. [WoS]
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  • [21] A. Sikorska-Nowak, Retarded functional differential equations in Banach spaces and Henstock-Kurzweil-Pettis integrals, Disscusiones Mathematicae, 27 (2007), 315-327.
  • [22] B. Wang, Dynamics of systems of infinite lattices, J. Differential Equations, 221 (2006), 224-245.
  • [23] B. Wang, Asymptotic behavior of non-autonomous lattice systems, J. Math. Anal. Appl,. 331 (2007), 121-136.
  • [24] W. Yan, Y. Li and Sh. Ji, Random attractors for first order stochastic retarded lattice dynamical systems, J. Math. Phys., 51 (2010), 17 pages. [WoS]
  • [25] C. Zhao and S. Zhou, Attractors of retarded first order lattice systems, Nonlinearity, 20 (2007), no. 8, 1987-2006. [Crossref][WoS]
  • [26] C. Zhao, Sh. Zhou, Sufficient conditions for the existence of global random attractors for stochastic lattice dynamical systems and applications, J. Math. Anal. Appl., 354 (2009), 78–95.
  • [27] C. Zhao, S. Zhou andW.Wang, Compact kernel sections for lattice systems with delays, Nonlinear Analysis TMA, 70 (2009), 1330-1348.
  • [28] S. Zhou, Attractors and approximations for lattice dynamical systems, J. Differential Equations, 200 (2004), 342-368. [WoS]
  • [29] S. Zhou, W. Shi, Attractors and dimension of dissipative lattice systems, J. Differential Equations, 224 (2006), 172-204.

Typ dokumentu

Bibliografia

Identyfikatory

Identyfikator YADDA

bwmeta1.element.doi-10_1515_msds-2015-0003
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