Decay properties for the Cauchy problem of the linear JMGT-viscoelastic plate with Cattaneo heat conduction

In this work, we investigate the Cauchy problem for the JMGT-viscoelastic plate system coupled with Cattaneo-type heat conduction. Our focus is on deriving optimal decay rate results for both the subcritical and critical regimes. Specifically, we improve upon the results in [Commun. Pure Appl. Anal. 2023] by showing that the decay behavior exhibits no regularity loss in the subcritical case. In contrast, a regularity-loss phenomenon arises in the critical case. Furthermore, we perform an asymptotic analysis of the eigenvalues to confirm the optimality of the decay rates in both scenarios.