Open AccessDynamics of piezoelectric beams with magnetic effects and delay term
Author(s) -
M. M. Freitas,
A. J. A. Ramos,
M. J. Dos Santos,
J.L.L. Almeida
Publication year - 2022
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.