Polynomial stability of thermoelastic Timoshenko system with non-global time-delayed Cattaneo's law

TL;DR

This paper investigates the stability of a thermoelastic Timoshenko system with a localized, delayed heat flux governed by Cattaneo's law, establishing well-posedness and polynomial decay of solutions.

Contribution

It introduces a new model with local, delayed heat flux in the Timoshenko system and proves its well-posedness and polynomial stability.

Findings

Proved well-posedness of the system

Established strong stability

Demonstrated polynomial decay of solutions

Abstract

In this paper, we consider a one dimensional thermoelastic Timoshenko system in which the heat flux is given by Cattaneo's law and acts locally on the bending moment with a time delay. We prove its well-posedness, strong stability, and polynomial stability.