DECAY-RATES FOR VISCOELASTIC PLATES WITH MEMORY

We consider the viscoelastic plate equation and we prove that the firs t and second order energies associated with its solution decay exponen tially provided the kernel of the convolution also decays exponentiall y. When the kernel decays polynomially then the energy also decays pol ynomially. More precisely if the kernel g satisfies 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) w ith p > 2, then the energy decays as 1/(1 + t)(p).