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Volume 4, Issue 2
Decay Structure of the Zener-Type Viscoelastic Plate with Type II Heat Conduction in the Whole Space

Etsuto Adachi, Ramon Quintanilla & Yoshihiro Ueda

DOI: 10.4208/cmaa.2025-0006

Commun. Math. Anal. Appl., 4 (2025), pp. 296-306.

Published online: 2025-06

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  • Abstract

In this paper, we study the Zener-type viscoelastic plate in that heat conduction is determined by the type II Green-Naghdi theory. This model considers the finite propagation of thermal waves, which is compatible with the causality principle. We consider the Cauchy problem of this model and derive the decay estimates of solutions. Furthermore, the optimality of the decay estimate is discussed.

  • Keywords

Zener-type viscoelastic plate, type II Green-Naghdi theory, dissipative structure.

  • AMS Subject Headings

35Q79, 74H40, 74K20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMAA-4-296, author = {Adachi , EtsutoQuintanilla , Ramon and Ueda , Yoshihiro}, title = {Decay Structure of the Zener-Type Viscoelastic Plate with Type II Heat Conduction in the Whole Space}, journal = {Communications in Mathematical Analysis and Applications}, year = {2025}, volume = {4}, number = {2}, pages = {296--306}, abstract = {

In this paper, we study the Zener-type viscoelastic plate in that heat conduction is determined by the type II Green-Naghdi theory. This model considers the finite propagation of thermal waves, which is compatible with the causality principle. We consider the Cauchy problem of this model and derive the decay estimates of solutions. Furthermore, the optimality of the decay estimate is discussed.

}, issn = {2790-1939}, doi = {https://doi.org/10.4208/cmaa.2025-0006}, url = {http://global-sci.org/intro/article_detail/cmaa/24125.html} }
TY - JOUR T1 - Decay Structure of the Zener-Type Viscoelastic Plate with Type II Heat Conduction in the Whole Space AU - Adachi , Etsuto AU - Quintanilla , Ramon AU - Ueda , Yoshihiro JO - Communications in Mathematical Analysis and Applications VL - 2 SP - 296 EP - 306 PY - 2025 DA - 2025/06 SN - 4 DO - http://doi.org/10.4208/cmaa.2025-0006 UR - https://global-sci.org/intro/article_detail/cmaa/24125.html KW - Zener-type viscoelastic plate, type II Green-Naghdi theory, dissipative structure. AB -

In this paper, we study the Zener-type viscoelastic plate in that heat conduction is determined by the type II Green-Naghdi theory. This model considers the finite propagation of thermal waves, which is compatible with the causality principle. We consider the Cauchy problem of this model and derive the decay estimates of solutions. Furthermore, the optimality of the decay estimate is discussed.

Adachi , EtsutoQuintanilla , Ramon and Ueda , Yoshihiro. (2025). Decay Structure of the Zener-Type Viscoelastic Plate with Type II Heat Conduction in the Whole Space. Communications in Mathematical Analysis and Applications. 4 (2). 296-306. doi:10.4208/cmaa.2025-0006
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