Decay energy for Reissner-Mindlin-Timoshenko system with delays terms

This article explores the asymptotic behavior of solutions to the Reissner-Mindlin-Timoshenko system, incorporating frictional dissipation and delay terms in the rotation angles. Using semigroup theory, we first establish the well-posedness of the system. We then analyze its stability properties, showing that the associated semigroup exhibits exponential stability when the wave speeds are equal. In contrast, for systems with different wave speeds, we prove that the energy decays polynomially. Our analysis relies on spectral methods to derive these stability results. Finally, to validate our theoretical findings, we present numerical solutions obtained from a series of experiments using the finite-difference method. These numerical results confirm the effectiveness of our analytical conclusions, providing a comprehensive understanding of the system’s behavior under varying conditions.