Transmission problems in (thermo-)viscoelasticity with Kelvin-Voigt damping : non-exponential, strong and polynomial stability

Munoz Rivera, Jaime E.; Racke, Reinhard

Transmission problems in (thermo-)viscoelasticity with Kelvin-Voigt damping : non-exponential, strong and polynomial stability

Files

Rivera_0-286046.pdf(349.76 KB)

Date

2015

Authors

Munoz Rivera, Jaime E.

Racke, Reinhard

Series

Konstanzer Schriften in Mathematik; 336

Publication type

Working Paper/Technical Report

Abstract

We investigate transmission problems between a (thermo-)viscoelastic system with Kelvin-Voigt damping, and a purely elastic system. It is shown that neither the elastic damping by Kelvin-Voigt mechanisms nor the dissipative effect of the temperature in one material can assure the exponential stability of the total system when it is coupled through transmission to a purely elastic system. The approach shows the lack of exponential stability using Weyl's theorem on perturbations of the essential spectrum. Instead, strong stability can be shown using the principle of unique continuation. To prove polynomial stability we provide an extended version of the characterizations by Borichev and Tomilov. Observations on the lack of compacity of the inverse of the arising semigroup generators are included too. The results apply to thermo-viscoelastic systems, to< purely elastic systems as well as to the scalar case consisting of wave equations.

Subject (DDC)

510 Mathematics

Cite This

ISO 690

MUNOZ RIVERA, Jaime E., Reinhard RACKE, 2015. Transmission problems in (thermo-)viscoelasticity with Kelvin-Voigt damping : non-exponential, strong and polynomial stability

BibTex

@techreport{MunozRivera2015Trans-30731,
  year={2015},
  series={Konstanzer Schriften in Mathematik},
  title={Transmission problems in (thermo-)viscoelasticity with Kelvin-Voigt damping : non-exponential, strong and polynomial stability},
  number={336},
  author={Munoz Rivera, Jaime E. and Racke, Reinhard}
}

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Bibliography of Konstanz

Yes