Abstract Theory of Multivalued Semiflows

  • Mikhail Z. Zgurovsky
  • Pavlo O. Kasyanov
  • Oleksiy V. Kapustyan
  • José Valero
  • Nina V. Zadoianchuk
Chapter
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 27)

Abstract

Beginning from the pioneering works [3, 52], the theory of global attractors of infinite-dimensional dynamical systems has become one of the main objects for investigation. Since then, deep results about existence, properties, structure, and dimension of global attractors for a wide class of dissipative systems have been obtained (see, e.g., [7, 38, 54, 75, 78]). For the application of this classical theory to partial and functional differential equations, it was necessary to have global existence and uniqueness of solutions of the Cauchy problem for all initial data of the phase space.

Keywords

Weak Solution Cauchy Problem Global Attractor Volterra System Bounded Open Subset 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Mikhail Z. Zgurovsky
    • 1
  • Pavlo O. Kasyanov
    • 2
  • Oleksiy V. Kapustyan
    • 2
  • José Valero
    • 3
  • Nina V. Zadoianchuk
    • 2
  1. 1.Institute for Applied System AnalysisNational Academy of Science National Technical University of UkraineKyivUkraine
  2. 2.Kyiv Polytechnic Institute Institute for Applied System AnalysisNational Technical University of UkraineKyivUkraine
  3. 3.Centro de Investigación OperativaUniv. Miguel Hernández de ElcheAlicanteSpain

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