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 tin time) of the energy, provi ded that suitable assumptions on the relaxation functions are given. N amely, if the relaxation decays exponentially then the first order ene rgy also decays exponentially. When the relaxation g satisfies -c(1)g( t)(1+1/p) less than or equal to g' (t) less than or equal to -c(0)g(t) (1+1/p); and g, g(1-1/p) is an element of L-1 (R) with p > 2 then the energy decays as 1/(1 + t)(p). A new Liapunov functional is built for this problem.