Global Attractors for Discontinuous Dynamical Systems with Multi-valued Impulsive Perturbations

  • Oleksiy V. KapustyanEmail author
  • Iryna V. Romaniuk
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 69)


In this work, we consider impulsive infinite-dimensional dynamical systems generated by parabolic equations with continuous bounded right-hand side and with impulsive multi-valued perturbations. Moments of impulses are not fixed and defined by moments of intersection of solutions with some subset of the phase space. We find an explicit formula in the case \(\varepsilon =0\) and prove that for sufficiently small value of the parameter \(\varepsilon >0\) the corresponding nonlinear system also has a global attractor.


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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Taras Shevchenko National University of KyivKyivUkraine
  2. 2.Institute for Applied System AnalysisNational Technical University of Ukraine “Kyiv Polytechnic Institute”KyivUkraine
  3. 3.Taras Shevchenko National University of KyivKyivUkraine

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