Decay rates for viscoelastic plates with memory

We consider the viscoelastic plate equation and we prove that the first and second order energies associated with its solution decay exponentially provided the kernel of the convolution also decays exponentially. When the kernel decays polynomially then the energy also decays polynomially. 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) with p > 2, then the energy decays as 1/(1 + t)(p).