Meccanica

, Volume 39, Issue 6, pp 547–561 | Cite as

Viscoelastic Solids of Exponential Type. II. Free Energies, Stability and Attractors

  • Mauro Fabrizio
  • Claudio Giorgi
  • Maria Grazia Naso
Article

Abstract.

The asymptotic behavior for solutions of the semilinear motion equation of a linear viscoelastic solid of exponential type (VSET) is studied and the existence of a global attractor is proved. These results are obtained by means of a suitable class of quadratic free energies defined on the minimal state space and making use of semigroup techniques. This is the second part of a plan which was started in a previous paper [6] by the study of state-space representation, minimality and controllability for VSET.

Keywords

Free energy Viscoelasticity Attractors Continuum mechanics 

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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Mauro Fabrizio
    • 1
  • Claudio Giorgi
    • 2
  • Maria Grazia Naso
    • 2
  1. 1.Dipartimento di Matematica, Facoltá di IngegneriaUniversitá di BolognaBolognaItalia
  2. 2.Dipartimento di Matematica, Facoltá di IngegneriaUniversitá di BresciaBresciaItalia

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