Energy decay of type III linear thermoelastic plates with memory

We analyze the decay properties of the solution semigroups generated by an abstract version of the linear systems { u t t + Δ 2 u + Δ α t = 0 α t t − Δ α − Δ α t − Δ u t = 0 and { u t t + Δ 2 u + Δ α t = 0 α t t − Δ α − ∫ 0 ∞ μ ( s ) Δ [ α ( t ) − α ( t − s ) ] d s − Δ u t = 0 ruling the evolution of linear thermoelastic plates within the theory of heat conduction of type III.