Existence of global attractors for impulsive dynamical systems

1Kapustyan, OV, 1Perestyuk, MO
1Taras Shevchenko National University of Kyiv
Dopov. Nac. akad. nauk Ukr. 2015, 12:13-18
https://doi.org/10.15407/dopovidi2015.12.013
Section: Mathematics
Language: Ukrainian
Abstract: 

The existence of global attractors for impulsive dynamical systems, which have trajectories with infinite number of impulsive perturbations, is investigated. We have proved the existence of a global attractor for a parabolic equation with nonlinear perturbation.

Keywords: global attractor, impulsive dynamical system, impulsive perturbation
References: 
  1. Samoilenko A. M., Perestyuk N. A. Differential equations with impulsive influence, Kyiv: Vyshcha Shkola, 1987 (in Russian).
  2. Samoilenko A. M., Perestyuk N. A. Impulsive differential equations, Singapore: World Scientific, 1995. https://doi.org/10.1142/2892
  3. Pavlidis T. Information and control, 1996, 9: 298–322. https://doi.org/10.1016/S0019-9958(66)90183-5
  4. Rozhko V. F. Differential Equations, 1975, 11, No 6: 1005–1012 (in Russian).
  5. Kaul S. K. J. Appl. Math. Stoch. Anal., 1994, 7, No 4: 509–523. https://doi.org/10.1155/S1048953394000390
  6. Bonotto E. M., Demuner D. P. Bull. Sci. Math., 2013, 137: 617–642. https://doi.org/10.1016/j.bulsci.2012.12.005
  7. Kapustyan A. V., Perestyuk N. A. Ukr. Math. J., 2003, 55, No 8: 1283–1294. https://doi.org/10.1023/B:UKMA.0000010759.30810.77
  8. Iovane G., Kapustyan O. V., Valero J. Nonlinear Analysis, 2008, 68: 2516–2530. https://doi.org/10.1016/j.na.2007.02.002
  9. Perestyuk M., Kapustyan O. Mem. Differential Equations Math. Phys., 2012, 56: 89–113.
  10. Kapustyan O. V., Kasyanov P. O., Valero J., Zgurovsky M. Z. Continuous and distributed systems, 2014, 211: 163–180.