DOI QR코드

DOI QR Code

EXISTENCE OF GLOBAL ATTRACTOR FOR CAUCHY PROBLEMS

  • Choi, Sung Kyu (Department of Mathematics Chungnam National University) ;
  • Jang, Hyun Ho (Department of Mathematics Chungnam National University) ;
  • Koo, Namjip (Department of Mathematics Chungnam National University) ;
  • Yun, Chanmi (Department of Mathematics Chungnam National University)
  • Received : 2013.06.01
  • Accepted : 2013.07.19
  • Published : 2013.08.15

Abstract

We investigate the existence of a global attractor for the Cauchy problem $$x^{\prime}(t)=Ax(t)+F(x(t)),\;x(0)=x_0{\in}X$$ on a Banach space X according to the remark in You and Yuan's paper.

Keywords

References

  1. M. Adimy and K. Ezzinbi, Local existence and linearized stability for partial functional differential equations, Dynam. Syst. Appl. 7 (1998), 389-403.
  2. J. Billotti and J. P. LaSalle, Dissipative periodic processes, Bull. Amer. Math. Soc. 77 (1971), 1082-1088. https://doi.org/10.1090/S0002-9904-1971-12879-3
  3. H. Bouzahir and K. Ezzinbi, Global attractor for a class of partial functional differential equations with infinite delay, in : T. Faria, P. Freitas(Eds.), Topics in Functional Difference Equations, Fields Inst. Commun., vol. 29, Amer. Math. Soc., Providence, RI, 2001, 63-71.
  4. H. Bouzahir, H. You, and R. Yuan, Global attractor for some partial functional differential equations with infinite delay, Funckcial. Ekvac. 54 (2011), 139-156. https://doi.org/10.1619/fesi.54.139
  5. T. Caraballo, P. Marin-Rubio, and J. Valero, Attractors for differential equations with unbounded delays, J. Differential Equations 239 (2007), 311-342. https://doi.org/10.1016/j.jde.2007.05.015
  6. J. Hale, Asymptotic Behavior of Dissipative Systems, Math. Surveys and Monographs, vol. 25, Amer. Math. Soc., Providence, RI, 1988.
  7. J. Hale and J. Kato, Phase space for retarded equations with infinite delay, Funkcial. Ekvac. 21 (1978), 11-41.
  8. H. Kellermann and M. Hieber, Integrated semigroup, J. Funct. Anal. 15 (1989), 160-180.
  9. A. Pazy, Semigroup of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci., vol. 44, Springer-Verlag, New York, 1983.
  10. H. R. Thieme, Semiflows generated by Lipschitz perturbations of non-densely defined operators, Differential Integral Equations 3 (1990), 1035-1066.
  11. H. You and R. Yuan, Global attractor for some partial functional differential equations with finite delay, Nonlinear Analysis 72 (2010), 3566-3574. https://doi.org/10.1016/j.na.2009.12.027
  12. M. C. Zelatti, On the theory of global attractors and Lyapunov functionals, Set-Valued Var. Anal. 21 (2013), 127-149. https://doi.org/10.1007/s11228-012-0215-2