Asian Journal of Mathematics and Computer Research

This paper investigates the polynomial stability of a thermoelastic Timoshenko system with Cattaneo’s heat conduction law. The system consists of coupled hyperbolic-parabolic equations governing the transverse displacement, rotation angle, temperature, and heat flux. Previous work established the lack of exponential stability regardless of the equal wave speeds (EWS) condition. It is proved in this paper that when the EWS condition is satisfied, the associated C0-semigroup exhibits polynomial stability. Specifically, it is demonstrated that solutions decay at a rate of t^−1/4 as t → ∞, with the decay rate uniform for initial data in the domain of the generator. The analysis employs energy methods combined with semigroup theory, leveraging the structural properties induced by the EWS condition to establish polynomial decay estimates. This result extends previous stability analyses and highlights the critical role of wave speed matching in stabilizing Timoshenko systems with second-sound thermal effects.