Decay rates of solutions to thermoviscoelastic plates with memory

We consider the thermoelastic plate 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 satisfies -c1g(t)1+1/p ⩽ g′(t) ⩽ -cog(t)1+1/p; and g,g1-1/p ∈ L1 (R) with p > 2 then the energy decays as 1/(1+t)p. A new Liapunov functional is built for this problem.