Stabilization of weakly coupled viscoelastic Kirchhoff plate and wave equations

TL;DR

This paper investigates the stabilization of a coupled system of viscoelastic Kirchhoff plate and wave equations, establishing explicit decay rates under general relaxation functions using multiplier methods.

Contribution

It introduces a new analysis for the stabilization of weakly coupled viscoelastic systems with general relaxation functions, providing explicit decay rate results.

Findings

Established explicit decay rates for the coupled system.

Extended the analysis to more general relaxation functions.

Applied multiplier methods and convex function properties.

Abstract

In this paper, we consider a weakly coupled system consisting of a viscoelastic Kirchhoff plate equation involving free boundary conditions and the viscoelastic wave equation with Dirichlet boundary conditions in a bounded domain. By assuming a more general type of relaxation functions, we establish explicit and general decay rate results, using the multiplier method and some properties of the convex functions.