Analysis of a laminated beam with dual-phase-lag thermoelasticity

This paper focuses on a thermoelastic laminated beam from both mathematical and numerical perspectives, where the dual-phase-lag heat conduction theory is used to model the heat transfer. In this theory, two delay parameters $ \tau_{\theta} $ and $ \tau_q $ are considered. Under the condition $ 2\tau_{\theta}>\tau_q $, we establish the well-posedness of the system and prove both exponential and polynomial stability results depending on the stability parameter $ \chi $. For the numerical study, we propose fully discrete approximations using the finite-element method combined with the implicit Euler scheme. Through this approach, we demonstrate discrete stability property and provide a priori error estimates. To showcase the accuracy of the approximation and illustrate the practical application of our theoretical findings, we present some numerical simulations.