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doi: 10.3934/eect.2021015

## Dynamics of piezoelectric beams with magnetic effects and delay term

 1 Faculty of Mathematics, Federal University of Pará, Raimundo Santana Street, S/N, 68721-000, Salinópolis, PA, Brazil 2 Faculty of Exact Sciences and Technology, Federal University of Pará, Manoel de Abre Street, S/N, 68440-000, Abaetetuba, PA, Brazil 3 Faculty of Petroleum Engineering, Federal University of Pará, Raimundo Santana Street, S/N, 68721-000, Salinópolis, PA, Brazil

* Corresponding author: Mirelson M. Freitas

Received  February 2020 Revised  December 2020 Published  April 2021

In this paper, we consider a piezoelectric beams system with magnetic effects and delay term. We study its long-time behavior through the associated dynamical system. We prove that the system is gradient and asymptotically smooth, which as a consequence, implies the existence of a global attractor, which is characterized as unstable manifold of the set of stationary solutions. We also get the quasi-stability of the system by establishing a stabilizability estimate and therefore obtain the finite fractal dimension of the global attractor.

Citation: Mirelson M. Freitas, Anderson J. A. Ramos, Manoel J. Dos Santos, Jamille L.L. Almeida. Dynamics of piezoelectric beams with magnetic effects and delay term. Evolution Equations & Control Theory, doi: 10.3934/eect.2021015
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