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Set-Valued and Variational Analysis

, Volume 21, Issue 2, pp 271–282 | Cite as

Regularity of Weak Solutions and Their Attractors for a Parabolic Feedback Control Problem

  • Pavlo O. Kasyanov
  • Luisa Toscano
  • Nina V. Zadoianchuk
Article

Abstract

We investigate additional regularity properties of all globally defined weak solutions, their global and trajectory attractors for a class of autonomous differential inclusion with upper semi-continuous interaction function, when initial data \(u_{\tau}\in L^2(\Omega)\). The main contributions of this paper are: (i) additional regularity and new topological properties of all weak solutions of parabolic feedback control problem with upper semi-continuous interaction function, (ii) a sufficient condition for regularity of global and trajectory attractors, and (iii) new a priory estimates for all weak solutions.

Keywords

Differential inclusion Global attractor Trajectory attractor Regularity Feedback control 

Mathematics Subject Classifications (2010)

34G25 34D45 35B65 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Pavlo O. Kasyanov
    • 1
  • Luisa Toscano
    • 2
  • Nina V. Zadoianchuk
    • 1
  1. 1.Institute for Applied System Analysis, National Technical University of Ukraine “Kyiv Polytechnic Institute”KyivUkraine
  2. 2.Dep. Math. and Appl.University of Naples “Federico II”NaplesItaly

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