DYNAMICS OF PIEZOELECTRIC BEAMS WITH MAGNETIC EFFECTS AND DELAY TERM
EVOLUTION EQUATIONS AND CONTROL THEORY(2022)
Abstract
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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Key words
 , Piezoelectric beams, Time delay, Magnetic effects, Quasi-stable sys-tem, Global attractor, Exponential attractors
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