Memory Effect on Decay Property of Solutions to Plate Equations

In this paper we focus on the initial-value problem of linear plate equations with memory in multi-dimensions, the decay structure of which is of regularity-loss property.We obtain fundamental solutions by using Fourier transform and Laplace transform.By virtue of the point-wise estimate of solutions in the Fourier space, we gain estimates and properties of solution operators, by utilizing which decay estimates of solutions to the linear problem are obtained and the decay rate can be as large as desired if the initial data are sufficiently smooth.