Dynamics of piezoelectric beams with magnetic effects and delay term

Mirelson M. Freitas; Anderson J. A. Ramos; Manoel J. Dos Santos; Jamille L.L. Almeida

doi:10.3934/eect.2021015

Article Contents

2022, Volume 11, Issue 2: 583-603. Doi: 10.3934/eect.2021015

This issue Previous Article Finite dimensional global attractor for a class of two-coupled nonlinear fractional Schrödinger equations Next Article Controllability of Hilfer fractional integro-differential equations of Sobolev-type with a nonlocal condition in a Banach space

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
^* Corresponding author: Mirelson M. Freitas

Received: January 31, 2020

Revised: November 30, 2020

Early access: April 2021

Published: April 2022

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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.

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Mathematics Subject Classification: Primary: 35B40, 35B41, 35L53; Secondary: 74K10.

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