Decay of solutions to an inertial model for a semilinear plate equation with memory

In this paper we focus on the initial value problem of an inertial model for a semilinear plate equation with memory in multi-dimensions (n≥1)(n≥1), which is of regularity-loss property. By using Fourier transform and Laplace transform, we obtain fundamental solutions to the corresponding linear problem and their pointwise estimates in the Fourier space. Appealing to this pointwise estimates, we obtain the global existence and the optimal decay estimates of solutions to the semilinear problem by employing the contraction mapping theorem.