Asymptotic Stability of Laminated Beams Under Maxwell–Cattaneo Thermoelastic Shear Effects

Abstract

In this work, we investigate the well-posedness and asymptotic behavior of a system of laminated beams subjected to thermal effects governed by the Maxwell–Cattaneo model, acting through the shear force. All results are established using the semigroup theory of linear operators. In particular, we apply the Gearhart–Huang–Prüss Theorem to prove that exponential decay occurs if and only if the stability number ${\mathrm{{\rm Y}}}_{\tau }$ vanishes. Otherwise, we invoke the Borichev–Tomilov Theorem to demonstrate polynomial decay. The results significantly enhance the understanding of the interplay between thermal relaxation governed by the Maxwell–Cattaneo law and structural mechanisms in the stabilization process, while also addressing a gap in the literature on the dynamic behavior of laminated beams under thermoelastic shear effects.