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Stability in Thermoviscoelasticity with Second Sound

  • G. Gómez Ávalos
  • J. Muñoz Rivera
  • O. Vera Villagran
Article
  • 75 Downloads

Abstract

Here we consider a string composed by three different materials: thermo elastic, viscoelastic and elastic. Our main result is that the exponential stability depends on the position of each material. That is, we prove that the model is exponentially stable if and only if the viscoelastic material is not in the center of the string. Otherwise, there is not exponential stability and the corresponding semigroup also goes to zero, but now polynomially.

Keywords

\(C_{0}\)-semigroup Exponential stability Thermo-viscoelasticity Viscoelasticity Kelvin-Voigt damping Stability of semigroups 

Notes

Acknowledgements

The authors thanks the research project of the Bio-Bio University: GI 171608/VC. Gerardo Gómez was supported by CONICYT-PCHA/doctorado nacional/2016-21160921.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • G. Gómez Ávalos
    • 1
  • J. Muñoz Rivera
    • 1
  • O. Vera Villagran
    • 1
  1. 1.DM. Universidad del Bío BíoConcepciónChile

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