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Polynomial stability of a magneto-thermoelastic Mindlin–Timoshenko plate model

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Abstract

In this paper, we consider the magneto-thermoelastic interactions in a two-dimensional Mindlin–Timoshenko plate. Our main result is concerned with the strong asymptotic stabilization of the model. In particular, we determine the rate of polynomial decay of the associated energy. In contrast with what was observed in other related articles, geometrical hypotheses on the plate configuration (such as radial symmetry) are not imposed in this study nor any kind of frictional damping mechanism. A suitable multiplier is instrumental in establishing the polynomial stability with the aid of a recent result due to Borichev and Tomilov (Math Ann 347(2):455–478, 2010).

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de Santa Maria, Santa Maria, RS, CEP 97105-900, Brazil

    Marcio V. Ferreira

  2. Departamento de Matemática, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, CEP 21941-909, Brazil

    Jaime E. Muñoz Rivera

  3. Laboratório Nacional de Computação Científica - LNCC, Petrópolis, RJ, CEP 25651-070, Brazil

    Jaime E. Muñoz Rivera

Authors
  1. Marcio V. Ferreira
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  2. Jaime E. Muñoz Rivera
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Corresponding author

Correspondence to Marcio V. Ferreira.

Additional information

This work was supported by CNPq, Grants 164793/2015-1 and 402689/2012-7.

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Ferreira, M.V., Muñoz Rivera, J.E. Polynomial stability of a magneto-thermoelastic Mindlin–Timoshenko plate model. Z. Angew. Math. Phys. 69, 3 (2018). https://doi.org/10.1007/s00033-017-0898-1

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  • DOI: https://doi.org/10.1007/s00033-017-0898-1

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