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On Global Attractors for Autonomous Damped Wave Equation with Discontinuous Nonlinearity

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Continuous and Distributed Systems

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

Abstract

We consider autonomous damped wave equation with discontinuous nonlinearity. The long-term prognosis of the state functions when the conditions on the parameters of the problem do not guarantee uniqueness of solution of the corresponding Cauchy problem are studied. We prove the existence of a global attractor and investigate its structure. It is obtained that trajectory of every weak solution defined on \([0;+\infty )\) tends to a fixed point.

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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 NAS, Kyiv Polytechnic Institute, National Technical University, Peremogy ave., 37, Kyiv, 03056, Ukraine

    Nataliia V. Gorban, Oleksiy V. Kapustyan, Pavlo O. Kasyanov & Liliia S. Paliichuk

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  1. Nataliia V. Gorban
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  2. Oleksiy V. Kapustyan
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  3. Pavlo O. Kasyanov
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  4. Liliia S. Paliichuk
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Correspondence to Nataliia V. Gorban .

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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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Gorban, N.V., Kapustyan, O.V., Kasyanov, P.O., Paliichuk, L.S. (2014). On Global Attractors for Autonomous Damped Wave Equation with Discontinuous Nonlinearity. 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_16

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  • DOI: https://doi.org/10.1007/978-3-319-03146-0_16

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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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