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On the Asymptotic Behavior of Thermoelastic Plate with Terms Concentrated in the Boundary

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Abstract

In this paper we consider autonomous thermoelastic plate systems with Neumann boundary conditions when some reaction terms are concentrated in a neighborhood of the boundary and this neighborhood shrinks to boundary as a parameter \(\varepsilon\) goes to zero. We present some remarks on asymptotic behavior of the global attractors which lead us to conclude the lower semicontinuity of this attractors at \(\varepsilon\) equal to zero. We also prove the finite-dimensionality of the attractors.

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Acknowledgements

The authors would like to thank the anonymous referees for their comments and suggestions which greatly improved the work.

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Authors and Affiliations

  1. Departamento de Ciências Exatas e da Terra, Universidade Federal de São Paulo, Diadema, SP, 09913-030, Brazil

    Gleiciane S. Aragão

  2. Departamento de Matemática, Universidade Federal da Paraíba, Cidade Universitária-Campus I, João Pessoa, PB, 58051-900, Brazil

    Flank D. M. Bezerra

  3. Centro de Ciências Humanas e Exatas, Universidade Estadual da Paraíba, Monteiro, PB, 58500-000, Brazil

    Cládio O. P. Da Silva

Authors
  1. Gleiciane S. Aragão
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  2. Flank D. M. Bezerra
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  3. Cládio O. P. Da Silva
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Correspondence to Cládio O. P. Da Silva.

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Research partially supported by CNPq # 303039/2021-3, Brazil.

Gleiciane S. Aragão partially supported by FAPESP 2019/04476-6, Brazil.

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Aragão, G.S., Bezerra, F.D.M. & Da Silva, C.O.P. On the Asymptotic Behavior of Thermoelastic Plate with Terms Concentrated in the Boundary. Differ Equ Dyn Syst (2022). https://doi.org/10.1007/s12591-022-00610-1

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