Stability and Eigenvalue Asymptotics of Multi-Dimensional Fully Magnetic Effected Piezoelectric System with Friction-Type Infinite Memory
Hai-E Zhang, Genqi Xu, Zhong‐Jie Han
Abstract
.The long time behavior of a kind of fully magnetic effected piezoelectric system is considered. The impact of the presence of only one friction-type infinite memory term on the stability of the piezoelectric coupled plate is investigated. By introducing the so called "minimal state variable" and using semigroup theories, the system is proved to be well-posed. It is found that this kind of memory term still acts as a damping to some extent under certain conditions, but its damping effect is too weak to indirectly stabilize the system exponentially. Based on frequency domain analysis, it is further proved that this system can be indirectly stabilized polynomially by only one friction-type infinite memory term located on one of these strongly coupled PDEs. Especially, the optimality of this decay rate is also further verified by detailed spectral analysis for the system operator.Keywordspiezoelectric system with magnetic effectpolynomial stabilityinfinite memoryfrequency domain methodoptimal decay rateeigenvalue asymptoticsMSC codes35B4035Q9370Q0574D9993C2093D15