Global attractor of an impulsive parabolic system

Authors

  • M.O. Perestyuk Taras Shevchenko National University of Kiev
  • O.V. Kapustyan Taras Shevchenko National University of Kiev
  • I.V. Romaniuk Київський нацiональний унiверситет iм. Тараса Шевченка

DOI:

https://doi.org/10.15407/dopovidi2017.05.003

Keywords:

global attractor, impulsive multivalued dynamical system, impulsive perturbation, parabolic system

Abstract

We study the existence of global attractors for impulsive multivalued dynamical systems, which have trajectories with infinite number of impulsive perturbations. The results are applied to a weakly nonlinear parabolic impulsive system.

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References

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Perestyuk, M. O. & Kapustyan, O. V. (2012). Long-time behaviour of evolution inclusion with non-damped impulsive effects. Mem. Differential Equations Math. Phys., 56, pp. 89-113.

Bonotto, E. M. & Demuner, D. P. (2013). Attractors of impulsive dissipative semidynamical systems. Bull. Sci. Math. 137, pp. 617-642. https://doi.org/10.1016/j.bulsci.2012.12.005

Kapustyan, O. V. & Perestyuk, M. O. (2015). Existence of global attractors for impulsive dynamical systems. Reports of the National Academy of Sciences of Ukraine, No. 12, pp. 13-18 (in Ukrainian). https://doi.org/10.15407/dopovidi2015.12.013

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Romaniuk, I. (2016). Global attractor for a multiform impulsive dynamic system. Bull. Taras Shevchenko Nat. Univ. of Kyiv, Ser. Math. Mech., Iss. 35, pp. 14-19 (in Ukrainian).

Chepyzhov, V. V. & Vishik, M. I. (2002). Attractors for equations of mathematical physics. Providence, RI: AMS.

Published

08.09.2024

How to Cite

Perestyuk, M., Kapustyan, O., & Romaniuk, I. (2024). Global attractor of an impulsive parabolic system . Reports of the National Academy of Sciences of Ukraine, (5), 3–7. https://doi.org/10.15407/dopovidi2017.05.003