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

Danhua Wang; Kewang Chen; Danhua Wang; Kewang Chen

doi:10.3934/math.2025547

AIMS Mathematics

2025, Volume 10, Issue 5: 12079-12091. doi: 10.3934/math.2025547

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Research article

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

Danhua Wang ^{1
,
,},
Kewang Chen ²

1.
College of Information Engineering, Nanjing Xiaozhuang University, Nanjing 211171, China
2.
School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China

Received: 14 March 2025 Revised: 04 May 2025 Accepted: 13 May 2025 Published: 26 May 2025
MSC : 35B40, 74F05, 74K20, 93D20

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.
- Decay estimate,
- JMGT equation,
- viscoelasticity,
- Cattaneo heat conduction,
- regularity-loss type
Citation: Danhua Wang, Kewang Chen. Decay properties for the Cauchy problem of the linear JMGT-viscoelastic plate with Cattaneo heat conduction[J]. AIMS Mathematics, 2025, 10(5): 12079-12091. doi: 10.3934/math.2025547

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Abstract

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.

References

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