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

TL;DR

This paper investigates the stability of solutions to a nonlinear viscoelastic plate with boundary frictional damping and a logarithmic source, extending previous models and improving stability results in the context of viscoelasticity.

Contribution

It introduces a new stability analysis for a viscoelastic plate with boundary frictional damping and a logarithmic source, extending prior models and results.

Findings

Established stability conditions for the viscoelastic plate solutions.

Extended previous models to include boundary frictional damping.

Improved earlier results on solution stability in viscoelastic problems.

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