Skip to main content
Log in

On the existence and the asymptotic stability of solutions for linearly viscoelastic solids

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. B. D. Coleman & W. Noll, Foundations of linear viscoelasticity, Rev. Mod. Phys. 33, 239–249 (1961).

    Google Scholar 

  2. B. D. Coleman & W. Noll, Simple fluid with fading memory, Proc. Int. Sympos. Second-order Effects, Haifa, 530–552, 1962.

  3. B. D. Coleman, On thermodynamics, strain impulses and viscoelasticity, Arch. Rational Mech. Anal. 17, 230–254 (1964).

    Google Scholar 

  4. V. Volterra, Sulle equazioni integrodifferenziali della teoria della elasticità, Atti Reale Accad. Lincei 18, n∘ 2, 295–302 (1909).

    Google Scholar 

  5. V. Volterra, Leçons sur les Functions des Lignes. Paris: Gauthier-Villars, 1928.

    Google Scholar 

  6. D. Graffi, Sui problemi delléreditarietà lineare, Nuovo Cimenta 5, 53–71 (1928).

    Google Scholar 

  7. G. Duvaut & J. Lions, Les Inéquations en Mécanique et en Physique. Dunod, Paris, 1972.

    Google Scholar 

  8. C. M. Dafermos, On abstract Volterra equations with applications to linear viscoelasticity, J. Diff. Eqs. 7, 554–569 (1970).

    Google Scholar 

  9. G. Fichera, Avere una Memoria tenaca crea gravi problemi, Arch. Rational Mech. Anal. 70, 101–112 (1979).

    Google Scholar 

  10. G. Fichera, Sul principio della memoria evanescente, Rend. Sem. Mat. Univ. Padova, 68, 245–259 (1982).

    Google Scholar 

  11. M. Fabrizio, An existence and uniqueness theorem in quasi-static viscoelasticity, Quart. Appl. Math. 47, 1–8 (1989).

    Google Scholar 

  12. B. D. Coleman & V. J. Mizel, A general theory of dissipation in materials with memory, Arch. Rational Mech. Anal. 27, 255–274 (1967).

    Google Scholar 

  13. C. M. Dafermos, Asymptotic stability in viscoelasticity, Arch. Rational Mech. Anal. 37, 297–308 (1970).

    Google Scholar 

  14. C. M. Dafermos, On the existence and asymptotic stability of solutions to the equations of linear thermoelasticity, Arch. Rational Mech. Anal. 29, 241–271 (1968).

    Google Scholar 

  15. M. Fabrizio & A. Morro, Viscoelastic relaxation function compatible with themodynamics, J. Elasticity 19, 63–75 (1988).

    Google Scholar 

  16. C. Giorgi, Alcune conseguenze delle restrizioni termodinamiche per mezzi viscoelastici lineari, Quad. Dip. Mat. Univ. Cattolica S. Cuore — Brescia 6 (1989).

  17. G. Fichera, Existence Theorems in Elasticity, Handbuch der Physik, Vol. VI. Springer-Verlag, Heidelberg, 347–389, 1972.

    Google Scholar 

  18. F. Treves, Basic Linear Partial Differential Equations, Academic Press, New York, 1975.

    Google Scholar 

  19. D. Graffi, Sull'espressione di alcune grandezze termodinamiche nei materiali con memoria, Rend. Sem. Mat. Univ. Padova 68, 17–29 (1982).

    Google Scholar 

  20. C. M. Dafermos, Contraction semigroups and trend to equilibrium in continuum mechanics. Proc. IUTAM/I.M.U. Conference of Applications of Functional Analysis to Mechanics 1975. Lecture Notes in Mathematics, 503, Springer-Verlag.

  21. R. Datko, Extending a Theorem of A. M. Liapunov to Hilbert Space, J. Math. Anal. Appl. 32, 610–616 (1970).

    Google Scholar 

  22. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Lecture Notes in Mathematics, 10, University of Maryland, 1974.

  23. W. A. Day, Time-reversal and the symmetry of the relaxation function of a linear viscoelastic material, Arch. Rational Mech. Anal. 40, 155–159 (1971).

    Google Scholar 

  24. B. Lazzari, Stability properties for non symmetric relaxation tensors in linear viscoelasticity (in press).

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by C. Dafermos

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fabrizio, M., Lazzari, B. On the existence and the asymptotic stability of solutions for linearly viscoelastic solids. Arch. Rational Mech. Anal. 116, 139–152 (1991). https://doi.org/10.1007/BF00375589

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00375589

Keywords

Navigation