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In this paper, we consider plate equations and investigate the interaction between a viscoelastic damping acting in the domain and a weak frictional damping localized on a part of the boundary or vice versa. The synchronous presence of two different types of dissipative effects will not improve the energy decay rates, but instead we prove that the energy decays at a rate dictated by the weaker damping. Under general assumptions on the damping terms, we establish, for the first time as per our knowledge, optimal and explicit formula for the energy decay rates of these systems.

Viscoelasticity versus nonlinear feedback in plate systems: optimal decay