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.
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AIMS Mathematics 2025, 10(5): 12079-12091
Published: 15 May 2025
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