Existence and Invariance of Global Attractors for Impulsive Parabolic System Without Uniqueness

  • Sergey Dashkovskiy
  • Petro Feketa
  • Oleksiy V. KapustyanEmail author
  • Iryna V. Romaniuk
Part of the Understanding Complex Systems book series (UCS)


In this paper, we apply the abstract theory of global attractors for multi-valued impulsive dynamical systems to weakly-nonlinear impulsively perturbed parabolic system without uniqueness of a solution to the Cauchy problem. We prove that for a sufficiently wide class of impulsive perturbations (including multi-valued ones) the global attractor of the corresponding multi-valued impulsive dynamical system has an invariant non-impulsive part.


Global Attractor Parabolic Systems Impulsive DS Impulsive Perturbations Multi-valued Ones 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was partially supported by the German Academic Exchange Service (DAAD). Oleksiy Kapustyan was partially supported by the State Fund For Fundamental Research, Grant of President of Ukraine.


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© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Sergey Dashkovskiy
    • 1
  • Petro Feketa
    • 2
  • Oleksiy V. Kapustyan
    • 3
    Email author
  • Iryna V. Romaniuk
    • 3
  1. 1.University of WürzburgWürzburgGermany
  2. 2.University of KaiserslauternKaiserslauternGermany
  3. 3.Taras Shevchenko National University of KyivKyivUkraine

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