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

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Advances in Dynamical Systems and Control

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 69))

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Abstract

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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Authors and Affiliations

  1. Taras Shevchenko National University of Kyiv, Volodymyrska Str., 64, Kyiv, 01601, Ukraine

    Oleksiy V. Kapustyan

  2. Institute for Applied System Analysis, National Technical University of Ukraine “Kyiv Polytechnic Institute”, Kyiv, Ukraine

    Oleksiy V. Kapustyan

  3. Taras Shevchenko National University of Kyiv, Akademika Glushkova Avenue, 4-e, Kyiv, 03127, Ukraine

    Iryna V. Romaniuk

Authors
  1. Oleksiy V. Kapustyan
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  2. Iryna V. Romaniuk
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Correspondence to Oleksiy V. Kapustyan .

Editor information

Editors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    Victor A. Sadovnichiy

  2. Kyiv Polytechnic Institute, National Technical University of Ukraine, Kiev, Ukraine

    Mikhail Z. Zgurovsky

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Kapustyan, O.V., Romaniuk, I.V. (2016). Global Attractors for Discontinuous Dynamical Systems with Multi-valued Impulsive Perturbations. In: Sadovnichiy, V., Zgurovsky, M. (eds) Advances in Dynamical Systems and Control. Studies in Systems, Decision and Control, vol 69. Springer, Cham. https://doi.org/10.1007/978-3-319-40673-2_9

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  • DOI: https://doi.org/10.1007/978-3-319-40673-2_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40672-5

  • Online ISBN: 978-3-319-40673-2

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