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Global well-posedness and exponential decay of fully dynamic and electrostatic or quasi-static piezoelectric beams subject to a neutral delay

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Abstract

In this paper, we consider a one-dimensional system of fully dynamic and electrostatic or quasi-static piezoelectric beams, where the mechanical equation is subject to a distributed delay of neutral type without any damping term. Under some assumptions, we first prove the global well-posedness of the system by using the classical Faedo-Galerkin approximations along with two a priori estimates. Next, based on the energy method and by constructing an appropriate Lyapunov functional we show that, despite delays are known to be of a destructive nature in the general case, this system is exponentially stable irrespective of any condition on the coefficients of the system.

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Acknowledgements

The authors would like to deeply thank the anonymous referees for their helpful observations and information that further improved our paper.

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Authors and Affiliations

  1. Laboratory of Mathematics, Informatics and Systems (LAMIS), Department of Mathematics and Computer Science, Echahid Cheikh Larbi Tebessi University, 12002, Tebessa, Algeria

    Sami Loucif & Rafik Guefaifia

  2. Department of Mathematics and Informatics, Univ Souk Ahras, P.O. Box 1553, 41000, Souk Ahras, Algeria

    Salah Zitouni

  3. Ecole Normale Supérieure d’enseignement Technologique, Skikda, Algeria

    Houssem Eddine Khochemane

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  1. Sami Loucif
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  2. Rafik Guefaifia
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Correspondence to Sami Loucif.

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Loucif, S., Guefaifia, R., Zitouni, S. et al. Global well-posedness and exponential decay of fully dynamic and electrostatic or quasi-static piezoelectric beams subject to a neutral delay. Z. Angew. Math. Phys. 74, 83 (2023). https://doi.org/10.1007/s00033-023-01972-4

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  • DOI: https://doi.org/10.1007/s00033-023-01972-4

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