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

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Modern Mathematics and Mechanics

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. University of Würzburg, Würzburg, Germany

    Sergey Dashkovskiy

  2. University of Kaiserslautern, Kaiserslautern, Germany

    Petro Feketa

  3. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Oleksiy V. Kapustyan & Iryna V. Romaniuk

Authors
  1. Sergey Dashkovskiy
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  2. Petro Feketa
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  3. Oleksiy V. Kapustyan
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  4. Iryna V. Romaniuk
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Corresponding author

Correspondence to Oleksiy V. Kapustyan .

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Editors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    Victor A. Sadovnichiy

  2. National Technical University of Ukraine, “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine

    Michael Z. Zgurovsky

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Dashkovskiy, S., Feketa, P., Kapustyan, O.V., Romaniuk, I.V. (2019). Existence and Invariance of Global Attractors for Impulsive Parabolic System Without Uniqueness. In: Sadovnichiy, V., Zgurovsky, M. (eds) Modern Mathematics and Mechanics. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-96755-4_4

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  • DOI: https://doi.org/10.1007/978-3-319-96755-4_4

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  • Online ISBN: 978-3-319-96755-4

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