Asymptotic Translation Uniform Integrability and Multivalued Dynamics of Solutions for Non-autonomous Reaction-Diffusion Equations

  • Michael Z. Zgurovsky
  • Pavlo O. Kasyanov
  • Nataliia V. Gorban
  • Liliia S. Paliichuk
Part of the Understanding Complex Systems book series (UCS)


In this note we introduce asymptotic translation uniform integrability condition for a function acting from a positive semi-axes of time-line to a Banach space. We prove that this condition is equivalent to uniform integrability condition. As a result, we obtain the corollaries for the multivalued dynamics (as time t → +) of solutions for non-autonomous reaction-diffusion equations.


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© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Michael Z. Zgurovsky
    • 1
  • Pavlo O. Kasyanov
    • 2
  • Nataliia V. Gorban
    • 2
  • Liliia S. Paliichuk
    • 2
  1. 1.National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”KyivUkraine
  2. 2.Institute for Applied System AnalysisNational Technical University of Ukraine, Igor Sikorsky Kyiv Politechnic InstituteKyivUkraine

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