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Attractors for Differential Inclusions and Their Applications for Evolution Algorithms

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System Analysis and Artificial Intelligence

Part of the book series: Studies in Computational Intelligence ((SCI,volume 1107))

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Abstract

In this paper we study the issues of global solvability and existence of global attractors for differential inclusion of parabolic type in the phase space of continuous functions with \(\sup \)-norm. Assuming an upper semicontinuity of the multi-valued right-hand side and sign condition of dissipativity we prove that all mild-solutions generate a multi-valued semiflow, and establish the existence of global attractor for the semiflow. We present also an evolutional algorithm for finding attractor elements.

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Author information

Authors and Affiliations

  1. Fakultät Bauingenieurwesen, Bauhaus-Universität Weimar, 99423, Weimar, Germany

    Nataliia Gorban

  2. Chair of Integral and Differential Equations, Taras Shevchenko National University of Kyiv, Volodymyrska Street, 64, Kyiv, 01601, Ukraine

    Oleksiy Kapustyan

  3. Institute for Applied System Analysis, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Beresteis’ky Ave., 37, Build, 1, Kyiv, 03056, Ukraine

    Pavlo Kasyanov

  4. Department of Information Engineering, Computer Science and Mathematics, University of L’Aquila, Via Vetoio, L’Aquila, 67100, Italy

    Bruno Rubino

Authors
  1. Nataliia Gorban
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  2. Oleksiy Kapustyan
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  3. Pavlo Kasyanov
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  4. Bruno Rubino
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Corresponding author

Correspondence to Oleksiy Kapustyan .

Editor information

Editors and Affiliations

  1. Research Supervisor of the Institute for Applied Systems Analysis, National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine

    Michael Zgurovsky

  2. Deputy Director for Research of the Institute for Applied Systems Analysis, National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine

    Nataliya Pankratova

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Gorban, N., Kapustyan, O., Kasyanov, P., Rubino, B. (2023). Attractors for Differential Inclusions and Their Applications for Evolution Algorithms. In: Zgurovsky, M., Pankratova, N. (eds) System Analysis and Artificial Intelligence . Studies in Computational Intelligence, vol 1107. Springer, Cham. https://doi.org/10.1007/978-3-031-37450-0_10

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