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

Files

Wang_2-6h1qempxz86l6.pdf(267.26 KB)

Date

2022

Authors

Wang, Danhua

Liu, Wenjun

Racke, Reinhard

Series

Konstanzer Schriften in Mathematik; 406

Publication type

Working Paper/Technical Report

Publication status

Submitted

Abstract

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.

Subject (DDC)

510 Mathematics

Cite This

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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Bibliography of Konstanz

Yes