Dynamics of piezoelectric beams with magnetic effects and delay term | Zendy

Mirelson M. Freitas | Zendy; A. J. A. Ramos | Zendy; M. J. Dos Santos | Zendy; J.L.L. Almeida | Zendy

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Dynamics of piezoelectric beams with magnetic effects and delay term

Author(s) -

Mirelson M. Freitas,

A. J. A. Ramos,

M. J. Dos Santos,

J.L.L. Almeida

Publication year - 2021

Publication title -

evolution equations and control theory

Language(s) - English

Resource type - Journals

eISSN - 2163-2480

pISSN - 2163-2472

DOI - 10.3934/eect.2021015

Subject(s) - attractor , term (time) , stability (learning theory) , manifold (fluid mechanics) , physics , fractal dimension , mathematical analysis , dimension (graph theory) , set (abstract data type) , dynamical system (definition) , mathematics , fractal , dynamical systems theory , statistical physics , pure mathematics , computer science , quantum mechanics , mechanical engineering , machine learning , engineering , programming language

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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