Exponential stability of Timoshenko-Gurtin-Pipkin systems with full thermal coupling

TL;DR

This paper proves exponential stability for a thermoelastic Timoshenko-Gurtin-Pipkin system with thermal coupling under various boundary conditions, regardless of structural parameters, using the history space framework.

Contribution

It establishes exponential stability of the system with full thermal coupling under different boundary conditions, a novel result in this context.

Findings

Solution semigroup is exponentially stable under mixed and full Dirichlet boundary conditions.

Stability holds independently of the structural parameters.

Uses the history space framework of Dafermos for analysis.

Abstract

We analyze the stability properties of a linear thermoelastic Timoshenko-Gurtin-Pipkin system with thermal coupling acting on both the shear force and the bending moment. Under either the mixed Dirichlet-Neumann or else the full Dirichlet boundary conditions, we show that the associated solution semigroup in the history space framework of Dafermos is exponentially stable independently of the values of the structural parameters of the model.