Fading memory spaces and approximate cycles in linear viscoelasticity

Mauro Fabrizio; Angelo Morro

Rendiconti del Seminario Matematico della Università di Padova (1989)

  • Volume: 82, page 239-255
  • ISSN: 0041-8994

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Fabrizio, Mauro, and Morro, Angelo. "Fading memory spaces and approximate cycles in linear viscoelasticity." Rendiconti del Seminario Matematico della Università di Padova 82 (1989): 239-255. <http://eudml.org/doc/108162>.

@article{Fabrizio1989,
author = {Fabrizio, Mauro, Morro, Angelo},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {linear isothermal viscoelasticity; approximate cycles; necessary and sufficient conditions; relaxation function},
language = {eng},
pages = {239-255},
publisher = {Seminario Matematico of the University of Padua},
title = {Fading memory spaces and approximate cycles in linear viscoelasticity},
url = {http://eudml.org/doc/108162},
volume = {82},
year = {1989},
}

TY - JOUR
AU - Fabrizio, Mauro
AU - Morro, Angelo
TI - Fading memory spaces and approximate cycles in linear viscoelasticity
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1989
PB - Seminario Matematico of the University of Padua
VL - 82
SP - 239
EP - 255
LA - eng
KW - linear isothermal viscoelasticity; approximate cycles; necessary and sufficient conditions; relaxation function
UR - http://eudml.org/doc/108162
ER -

References

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  1. [1] M. Fabrizio - A. Morro, Thermodynamic restrictions on relaxation functions in linear viscoelasticity, Mech. Res. Comm., 12 (1985), pp. 101-105. 
  2. [2] A. Morro - M. FABRIZIO, On uniqueness in linear viscoelasticity: a family of counterexamples, Quart. Appl. Math., 45 (1987), pp. 321-325. Zbl0621.73039MR895102
  3. [3] L. Boltzmann, Zur Theorie der elastischen Nachwirkung, Sitzber. Kaiserl. Akad. Wiss. Wien, Math.-Naturw. Kl., 70 (1874), pp. 275-306. JFM06.0648.02
  4. [4] V. Volterra, Sur les equations intégro-difféerentielles et leurs applications, Acta Mathem., 35 (1912), pp. 295-356. Zbl43.0431.03MR1555080JFM43.0431.03
  5. [5] D. Graffi, Sopra alcuni fenomeni ereditari dell'elettrologia, Rend. Istit. Lombardo Scienze Lettere, Serie II, 68-69 (1936), pp. 124-139. Zbl0015.13802
  6. [6] D.R. Bland, The Theory of Linear Viscoelasticity, Pergamon, New York (1960). Zbl0108.38501MR110314
  7. [7] M.E. Gurtin - E. STERNBERG, On the linear theory of viscoelasticity, Arch. Rational Mech. Anal., 11 (1962), pp. 291-356. Zbl0107.41007MR147047
  8. [8] M.J. Leitman - G.M.C. Fisher, The Linear Theory of Viscoelasticity, in Encyclopedia of Physics, VIa/3, Springer, Berlin (1973). 
  9. [9] B.D. Coleman - W. Noll, Foundations of linear viscoelasticity, Rev. Mod. Phys., 33 (1961), pp. 239-249. Zbl0103.40804MR158605
  10. [10] B.D. Coleman, Thermodynamics of materials with memory, Arch. Rational Mech. Anal., 17 (1964), pp. 1-46. MR171419
  11. [11] B.D. Coleman, On thermodynamics, strain impulses and viscoelasticity, Arch. Rational Mech. Anal., 17 (1964), pp. 230-254. Zbl0125.13603MR171420
  12. [12] W.A. Day, Restrictions on relaxation functions in linear viscoelasticity, Quart. J. Mech. Appl. Math., 24 (1971), pp. 487-497. Zbl0241.73035MR317631
  13. [13] D. Graffi, Sui problemi della ereditarietà lineare, Nuovo Cimento, 5 (1928), pp. 53-71. JFM54.0882.02
  14. [14] B.D. Coleman - V.J. Mizel, Norms and semi-groups in the theory of fading memory, Arch. Rational Mech. Anal., 23 (1966), pp. 87-123. Zbl0146.46104MR210343
  15. [15] B.D. Coleman - D.R. Owen, A mathematical foundation for thermodynamics, Arch. Rational Mech. Anal., 54 (1974), pp. 1-104. Zbl0306.73004MR395502
  16. [16] M. Fabrizio - A. Morro, Viscoelastic relaxation functions compatible with thermodynamics, J. Elasticity, 19 (1988), pp. 63-75. Zbl0661.73019MR928727
  17. [17] C. Truesdell, Rational Thermodynamics, Springer, New York (1984); Appendix G1 by B. D. Coleman and D. R. Owen. Zbl0559.00016MR766401

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