Decay rates of solutions to a von Kármán system for viscoelastic plates with memory

We consider the dynamical von Kármán equations for viscoelastic plates under the presence of a long-range memory. We find uniform rates of decay (in time) of the energy, provided that suitable assumptions on the relaxation functions are given. Namely, if the relaxation decays exponentially, then the first-order energy also decays exponentially, When the relaxation g g satisfies \[ − c 1 g 1 + 1 p ( t ) ≤ g ′ ( t ) ≤ − c 0 g ( t ) 1 + 1 p , 0 ≤ g ( t ) ≤ c 2 g 1 + 1 p ( t ) , and - {c_1}{g1 + 1/p} ( t ) ≤ g’ ( t ) ≤ - {c_0}g{ ( t )1 + 1/p}, 0 ≤ g ( t ) ≤ {c_2}{g1 + 1/p} ( t ) , \: and \] \[ g , g 1 + 1 p ∈ L 1 ( R ) with p > 2 ,