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

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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.

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Authors and Affiliations

  1. Institute for Applied System Analysis, National Technical University of Ukraine “Kyiv Polytechnic Institute”, Peremogy Ave., 37, Build, 35, 03056, Kyiv, Ukraine

    Pavlo O. Kasyanov & Nina V. Zadoianchuk

  2. Dep. Math. and Appl., University of Naples “Federico II”, R. Caccioppoli, via Claudio 21, 80125, Naples, Italy

    Luisa Toscano

Authors
  1. Pavlo O. Kasyanov
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  2. Luisa Toscano
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  3. Nina V. Zadoianchuk
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Correspondence to Pavlo O. Kasyanov.

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Kasyanov, P.O., Toscano, L. & Zadoianchuk, N.V. Regularity of Weak Solutions and Their Attractors for a Parabolic Feedback Control Problem. Set-Valued Var. Anal 21, 271–282 (2013). https://doi.org/10.1007/s11228-013-0233-8

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  • DOI: https://doi.org/10.1007/s11228-013-0233-8

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