Stability results for viscoelastic wave equation with dynamic boundary conditions

TL;DR

This paper investigates the stability of a viscoelastic wave equation with dynamic boundary conditions, establishing energy decay results using frequency domain methods and resolvent analysis under specific assumptions.

Contribution

It introduces new stability results for viscoelastic wave equations with dynamic boundary conditions using a novel combination of contradiction and resolvent analysis methods.

Findings

Established general energy decay rates for the wave equation.

Applied frequency domain method to analyze stability.

Provided conditions on the relaxation function for decay.

Abstract

In this paper we consider wave viscoelastic equation with dynamic boundary condition in a bounded domain, we establish a general decay result of energy by exploiting the frequency domain method which consists in combining a contradiction argument and a special analysis for the resolvent of the operator of interest with assumptions on past history relaxation function.