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Continuous and Distributed Systems pp 149–162Cite as

Multivalued Dynamics of Solutions for Autonomous Operator Differential Equations in Strongest Topologies

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Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 211))

Abstract

We consider nonlinear autonomous operator differential equations with pseudomonotone interaction functions satisfying \((S)\)-property. The dynamics of all weak solutions on the positive time semi-axis is studied. We prove the existence of a trajectory and a global attractor in a strongest topologies and study their structure. As a possible application, we consider the class of high-order nonlinear parabolic equations.

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Acknowledgments

This work was partially supported by the Ukrainian State Fund for Fundamental Researches under grants GP/F44/076, GP/F49/070, and by the NAS of Ukraine under grant 2273/13.

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Authors and Affiliations

  1. Institute for Applied System Analysis, National Technical University of Ukraine “Kyiv Polytechnic Institute”, Peremogy ave., 37, build, 35,  Kyiv,  03056, Ukraine

    Mikhail Z. Zgurovsky & Pavlo O. Kasyanov

Authors
  1. Mikhail Z. Zgurovsky
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  2. Pavlo O. Kasyanov
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Correspondence to Pavlo O. Kasyanov .

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Editors and Affiliations

  1. National Academy of Science, National Technical University of Ukraine, Kiev, Ukraine

    Mikhail Z. Zgurovsky

  2. Lomonosov Moscow State University, Moscow, Russia

    Victor A. Sadovnichiy

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Zgurovsky, M.Z., Kasyanov, P.O. (2014). Multivalued Dynamics of Solutions for Autonomous Operator Differential Equations in Strongest Topologies. In: Zgurovsky, M., Sadovnichiy, V. (eds) Continuous and Distributed Systems. Solid Mechanics and Its Applications, vol 211. Springer, Cham. https://doi.org/10.1007/978-3-319-03146-0_11

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  • DOI: https://doi.org/10.1007/978-3-319-03146-0_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03145-3

  • Online ISBN: 978-3-319-03146-0

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