Exponential Decay in a Timoshenko-type System of Thermoelasticity of Type III with Frictional versus Viscoelatic Damping and Delay

TL;DR

This paper investigates the exponential decay behavior of a Timoshenko-type thermoelastic system with frictional and viscoelastic damping, establishing conditions for global existence and decay using energy methods and Lyapunov functionals.

Contribution

It introduces a novel analysis of Type-III thermoelastic Timoshenko systems with different damping mechanisms, proving exponential decay under specific boundary conditions.

Findings

Proved global existence of solutions.

Established exponential decay rates.

Compared effects of frictional and viscoelastic damping.

Abstract

In this work, a Timoshenko system of type III of thermoelasticity with frictional versus viscoelastic under Dirichlet-Dirichlet-Neumann boundary conditions was considered. By exploiting energy method to produce a suitable Lyapunov functional, we establish the global existence, exponential decay of Type-III case.