Long time dynamics and upper semi-continuity of attractors for piezoelectric beams with nonlinear boundary feedback

A system of boundary-controlled piezoelectric beam equations, accounting for the interactions between mechanical vibrations and fully-dynamic electromagnetic fields, is considered. Even though electrostatic quasi-static field approximations Maxwell’s equations are sufficient most models systems, where magnetic permeability completely discarded, PDE model considered here retains pronounced wave behavior fields to accurately describe dynamics acoustic devices. It also crucial investigate whether closed-loop with nonlinear state feedback external sources, close one described by electrostatic/quasi-static when μ small. Therefore, asymptotic analyzed at first. The existence global attractors finite fractal dimension exponential proved. Finally, upper-semicontinuity respect ones shown.