Annali di Matematica Pura ed Applicata

, Volume 178, Issue 1, pp 45–66 | Cite as

Exponential stability of a linear viscoelastic bar with thermal memory

  • Claudio Giorgi
  • Maria Grazia Naso
Article

Abstract

In this paper we study a one-dimensional evolution problem arising in the theory of linear thermoviscoelasticity with hereditary heat conduction. Depending on the istantaneous conductivity K0, both Coleman-Gurtin (K0>0) and Gurtin-Pipkin (K0=0) heat flow theories are involved. In any case, the exponential stability of the corresponding semigroup is proved for a class of memory functions including weakly singular kernels. In order to achieve the exponential decay of the energy, we assume that mechanical and thermal memory kernels decay exponentially for large time.

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Copyright information

© Fondazione Annali di Matematica Pure ed Applicata 2000

Authors and Affiliations

  • Claudio Giorgi
    • 1
  • Maria Grazia Naso
    • 2
  1. 1.Dipartimento di Elettronica per l'AutomazioneUniversità degli Studi di BresciaBresciaItalia
  2. 2.Dipartimento di MatematicaUniversità Cattolica del Sacro CuoreBresciaItalia

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