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An inverse inequality for a Bresse–Timoshenko system without second spectrum of frequency

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Abstract

In this paper, we consider a truncated version of the Timoshenko beam model and we prove an inverse inequality in order to obtain the controllability of the total system. The present system is new in the control and stabilization setting according to recent contributions due to Almeida Júnior and Ramos (Z Angew Math Phys 68(145):31, 2017). The advantage here relies on mathematical results which do not depend on the classical condition between wave propagation velocities.

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Acknowledgements

The authors are grateful to the referee for his/her constructive remarks, which have enhanced the presentation of this paper.

Funding

A.J.A. Ramos thanks the CNPq for financial support through the projects: “Asymptotic stabilization and numerical treatment for carbon nanotubes” - CNPq Grant 310729/2019-0.

D.S. Almeida Júnior thanks CNPq and CAPES/INCTMAT/LNCC for support through Grants 310423/2016-3 and 88887.351763/2019-00, respectively. L.G.R. Miranda thanks the Capes for financial scholarship support through Grant 99244292220.

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Authors and Affiliations

  1. Faculty of Mathematics, Federal University of Pará, Raimundo Santana Street, s/n, Salinópolis, Pará,  68721-000, Brazil

    A. J. A. Ramos

  2. Federal University of Pará, Augusto Corrêa Street, 01, Belém, Pará,  66075-110, Brazil

    D. S. Almeida Júnior & L. G. R. Miranda

Authors
  1. A. J. A. Ramos
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  2. D. S. Almeida Júnior
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  3. L. G. R. Miranda
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Correspondence to A. J. A. Ramos.

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Ramos, A.J.A., Júnior, D.S.A. & Miranda, L.G.R. An inverse inequality for a Bresse–Timoshenko system without second spectrum of frequency. Arch. Math. 114, 709–719 (2020). https://doi.org/10.1007/s00013-020-01452-5

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  • DOI: https://doi.org/10.1007/s00013-020-01452-5

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