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

Wang, Danhua; Liu, Wenjun; Racke, Reinhard

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

Dateien

Wang_2-6h1qempxz86l6.pdfGröße: 267.26 KBDownloads: 102

Datum

2022

Autor:innen

Wang, Danhua

Liu, Wenjun

Racke, Reinhard

Open Access-Veröffentlichung

Open Access Green

Sammlungen

Mathematik und Statistik

Publikationstyp

Working Paper/Technical Report

Publikationsstatus

Submitted

Zusammenfassung

We consider the Cauchy problem related to the JMGT-viscoelastic plate coupled with a heat equation with two kinds of thermal laws, which are thermoelasticity of type III and the Gurtin-Pipkin thermal law, respectively. We prove optimal results on decay rates for both the thermoelasticity type III system and the Gurtin-Pipkin thermal law system. More precisely, for the type III system, we show that the decay property is not of regularity-loss type in both the subcritical and critical cases. The result matches with the system in a bounded domain, where the system is known to be exponentially stable in the subcritical case. For the Gurtin-Pipkin thermal law system, there is a regularity-loss phenomenon in the critical case. We also study the asymptotic expansion of the eigenvalues to prove the optimality of the obtained decay rates for both models.

Fachgebiet (DDC)

510 Mathematik

Zitieren

ISO 690

WANG, Danhua, Wenjun LIU, Reinhard RACKE, 2022. Decay properties for the Cauchy problem of the linear JMGT-viscoelastic plate with heat conduction

BibTex

@techreport{Wang2022Decay-58876,
  year={2022},
  series={Konstanzer Schriften in Mathematik},
  title={Decay properties for the Cauchy problem of the linear JMGT-viscoelastic plate with heat conduction},
  number={406},
  author={Wang, Danhua and Liu, Wenjun and Racke, Reinhard}
}

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