Optimal decay for plates with rotational inertia and memory

We study the asymptotic behavior of a linear plate equation with effects of rotational inertia and a fractional damping in the memory term: where and the kernel g is exponentially decreasing. The main result of this work is the polynomial decay of their solutions when . We prove that the solutions decay with the rate and also that the decay rate is optimal. Furthermore, when , we obtain the exponential decay of the solutions.