Asymptotic behavior of solutions to a nonlinear plate equation with memory

In this paper we consider the initial value problem of a nonlinear plate equation with memory-type dissipation in multi-dimensional space. Due to the memory effect, more technique is needed to deal with the global existence and decay property of solutions compared with the frictional dissipation. The model we study is an inertial one and the rotational inertia plays an important role in the part of energy estimates. By exploiting the time-weighted energy method we prove the global existence and asymptotic decay of solutions under smallness and suitable regularity assumptions on the initial data.