On the Control of Solutions of a Viscoelastic Plate Problem with a Frictional Damping Term

In this article, we study the stability of solutions to a nonlinear viscoelastic plate problem with frictional damping of a memory on a part of the boundary, and a logarithmic source in a bounded domain $\mathrm{\Omega }\subset {\mathbb{R}}^2\mathrm{.}$ In this problem the relaxation function $r$ satisfies $r^{\mathrm{\prime }}\left(t\right)\le -h\left(t\right)\mathcal{G}\left(r\left(t\right)\right)$ for all $t\ge 0$, where $h$ is a nonincreasing positive function. This work extends previous works with viscoelastic plate problems and improves earlier results in the