Analytical Study and Numerical Test of a Heat Bresse Timoshenko system

Abstract

This study investigates a one-dimensional Bresse–Timoshenko beam model incorporating microtem-

perature effects and viscous damping on the transverse displacement of the structure. The global well-posedness of the model is established using the Faedo–Galerkin approximation method alongside rigorous analytical estimates. A Lyapunov functional constructed through the multiplier method enables the proof that the total energy of the system decays exponentially over time, irrespective of the wave propagation speeds or specific parameter values. To corroborate the theoretical findings, numerical simulations are conducted using an explicit Euler scheme for time discretization and the classical finite difference method for spatial discretization. Two numerical examples are provided to illustrate the accuracy and relevance of the theoretical results.