A note on exponential stability of a thermoelastic system with internal delay

TL;DR

This paper investigates the exponential stability of a thermoelastic system with internal delay, enhanced by Kelvin-Voigt damping, using frequency domain methods to improve previous stability results.

Contribution

It introduces Kelvin-Voigt damping to a delayed thermoelastic system and proves its exponential stability, extending prior work on well-posedness and stability.

Findings

System with damping is exponentially stable

Frequency domain method effectively proves stability

Improves previous stability results for delayed systems

Abstract

The presence of a delay in a thermoelastic system destroys the well-posedness and the stabilizing effect of the heat conduction. To avoid this problem we add to the system, at the delayed equation, a Kelvin-Voigt damping. In this note we point on the exponential stability of such system in order to improve the mean result in our paper Well-posedness and exponential stability of a thermoelastic system with internal delay (Applicable Analysis J 101, 4851-4865, 2022). We use a frequency domain method in the proof of stability.