Stability of an abstract-wave equation with delay and a Kelvin-Voigt damping

TL;DR

This paper investigates the stabilization of an abstract-wave equation with delay using Kelvin-Voigt damping, demonstrating exponential stability through a frequency-domain approach.

Contribution

It provides a new exponential stability result for wave equations with delay and Kelvin-Voigt damping, expanding understanding of delayed PDE stabilization.

Findings

Exponential stability achieved under certain damping conditions

Frequency-domain method effectively proves stability

Delay effects are managed within the damping framework

Abstract

In this paper we consider a stabilization problem for the abstract-wave equation with delay. We prove an exponential stability result for appropriate damping coefficient. The proof of the main result is based on a frequency-domain approach.