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

Abstract

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 $\Omega \subset \mathbb{R}^2.$ In this problem the relaxation function $r$ satisfies $r^{\prime}\left( t\right)\leq -h\left( t\right) \mathcal{G}\left( r\left( t\right) \right)$ for all $t\geq 0$, where $h$ is a nonincreasing positive function. This work extends previous works with viscoelastic plate problems and improves earlier results in the