Asymptotic Behavior of a Mindlin-Timoshenko Plate with Viscoelastic Dissipation on the Boundary

Abstract

A Mindlin-Timoshenko plate system with memory dissipation on the boundary is considered and the asymptotic behavior of the energy when the time goes to infinity is showed, more precisely, we prove that the energy decays with the same rate as the relaxation function, that is, if the relaxation function decay exponentially (respectively polynomially) then the energy decay exponentially (respectively polynomially).