Asymptotic behavior and numerical analysis for a thermoelastic-Bresse system with second sound

Resumo

In this study, we investigate the behavior of a linear one-dimensional thermoelastic Bresse system that incorporates second sound phenomena. We begin by establishing that the system is well-posed and identifying the conditions necessary for it to demonstrate exponential stability, which depend on certain parameters of the system. Our proof utilizes semigroup theory and a hybrid methodology that combines energy techniques with frequency domain analysis. Subsequently, we introduce a nite element approximation for the system and demonstrate that the associated discrete energy decreases over time. Additionally, we derive several a priori error estimates to assess the accuracy of our approximation. Finally, we validate our theoretical ndings by demonstrating that the numerical results align with our established theoretical predictions.