Regularity and asymptotic behaviour for a damped plate-membrane transmission problem

Stabilization for vibrating plate with singular structural damping

“…It is shown in this work that the damping supported near the whole boundary is strong enough to produce uniform exponential decay of the energy of the coupled system. Noting as well the paper of Denk et al [22] in which they consider a transmission problem where a structurally damped plate equation is coupled with a damped or undamped wave equation by transmission conditions. They show that exponential stability holds in the damped-damped situation and polynomial stability (but no exponential stability) holds in the damped-undamped case.…”

“…The study of the stabilization of problem involving constructive viscoelastic damping has attached a lot of attention in recent years e.g. [1,3,4,2,9,10,13,14,15,19,20,21,25,26] for the case of the Kelvin-Voigt damping and [11,22,27] for the case of the locally distributed structural damping. Noting that the main difference between these two kinds of damping from a mathematical point of view is that the Kelvin-Voigt damping is an operator of the same order of the leading elastic term while the structural order is of the half of the order of the principal operator.…”