Classical Free Energies of a Heat Conductor with Memory and the Minimum Free Energy for its Discrete Spectrum Model

Giovambattista Amendola; Sandra Carillo; Adele Manes

Bollettino dell'Unione Matematica Italiana (2010)

  • Volume: 3, Issue: 3, page 421-446
  • ISSN: 0392-4041

Abstract

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Free energies, originally proposed for viscoelastic solids, together with their corresponding internal dissipations, are here considered under forms adapted to the case of rigid heat conductors with memory. The results related to the minimum free energy of the discrete spectrum model are then compared with some of the classical free energies of such conductors.

How to cite

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Amendola, Giovambattista, Carillo, Sandra, and Manes, Adele. "Classical Free Energies of a Heat Conductor with Memory and the Minimum Free Energy for its Discrete Spectrum Model." Bollettino dell'Unione Matematica Italiana 3.3 (2010): 421-446. <http://eudml.org/doc/290674>.

@article{Amendola2010,
abstract = {Free energies, originally proposed for viscoelastic solids, together with their corresponding internal dissipations, are here considered under forms adapted to the case of rigid heat conductors with memory. The results related to the minimum free energy of the discrete spectrum model are then compared with some of the classical free energies of such conductors.},
author = {Amendola, Giovambattista, Carillo, Sandra, Manes, Adele},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {421-446},
publisher = {Unione Matematica Italiana},
title = {Classical Free Energies of a Heat Conductor with Memory and the Minimum Free Energy for its Discrete Spectrum Model},
url = {http://eudml.org/doc/290674},
volume = {3},
year = {2010},
}

TY - JOUR
AU - Amendola, Giovambattista
AU - Carillo, Sandra
AU - Manes, Adele
TI - Classical Free Energies of a Heat Conductor with Memory and the Minimum Free Energy for its Discrete Spectrum Model
JO - Bollettino dell'Unione Matematica Italiana
DA - 2010/10//
PB - Unione Matematica Italiana
VL - 3
IS - 3
SP - 421
EP - 446
AB - Free energies, originally proposed for viscoelastic solids, together with their corresponding internal dissipations, are here considered under forms adapted to the case of rigid heat conductors with memory. The results related to the minimum free energy of the discrete spectrum model are then compared with some of the classical free energies of such conductors.
LA - eng
UR - http://eudml.org/doc/290674
ER -

References

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  1. AMENDOLA, G. - BOSELLO, C. A. - FABRIZIO, M., Maximum recoverable work and pseudofree energies for a rigid heat conductor, Nonlinear Oscillations, 10 (1) (2007), 7-25. Zbl1268.80004MR2357060DOI10.1007/s11072-007-0002-4
  2. AMENDOLA, G. - BOSELLO, C. A. - MANES, A., On free energies for a heat conductor with memory effects, to appear. 
  3. AMENDOLA, G. - CARILLO, S., Thermal work and minimum free energy in a heat conductor with memory, Quart. J. of Mech. and Appl. Math., 57 (3) (2004), 429-446. Zbl1151.80301MR2088844DOI10.1093/qjmam/57.3.429
  4. AMENDOLA, G. - FABRIZIO, M. - GOLDEN, J. M., Free energies for a rigid heat conductor with memory, IMA J. Appl. Math. (2010). Zbl05844402MR2740035DOI10.1093/imamat/hxq012
  5. AMENDOLA, G. - MANES, A., Minimum free energy for a rigid heat conductor with memory and application to a discrete spectrum model, Boll. Un. Mat. Italiana, 8 (10B) (2007), 969-987. Zbl1183.80008MR2507909
  6. AMENDOLA, G. - MANES, A. - VETTORI, C., Maximum recoverable work for a rigid heat conductor with memory, Acta Applicandae Mathematicae, 110, issue 3 (2010), 1011-1036. Zbl1206.80004MR2639155DOI10.1007/s10440-009-9491-8
  7. BREUR, S. - ONAT, E. T., On the determination of free energy in linear viscoelasticity, Z. Angew. Math. Phys., 15 (1964), 184-191. Zbl0123.40802MR178645DOI10.1007/BF01602660
  8. CATTANEO, C., Sulla conduzione del calore, Atti Sem. Mat. Fis. Univ. Modena, 3 (1948), 83-101. MR32898
  9. CARILLO, S., Some remarks on materials with memory: heat conduction and viscoelasticity, J. Nonlinear Math. Phys., 12, suppl. 1 (2005), 163-178. Zbl1362.74015MR2117178DOI10.2991/jnmp.2005.12.s1.14
  10. DAY, W. A., Reversibility, recoverable work and free energy in linear viscoelasticity, Quart. J. Mech. and Appl. Math., 23 (1970), 1-15. Zbl0219.73040MR273881DOI10.1093/qjmam/23.4.469
  11. DESERI, L. - FABRIZIO, M. - GOLDEN, J. M., The concept of a minimal state in viscoelasticity: new free energies and applications to PDEs, Arch. Rational Mech. Anal., 181 (1) (2006), 43-96. Zbl1152.74323MR2221203DOI10.1007/s00205-005-0406-1
  12. DILL, E. D., Simple materials with fading memory, In: Continuum Physics II., Academic, Berlin, 1972. 
  13. FABRIZIO, M. - MORRO, A., Mathematical problems in linear viscoelasticity, SIAM, Philadelphia, 1992. Zbl0753.73003MR1153021DOI10.1137/1.9781611970807
  14. GIORGI, C. - GENTILI, G., Thermodynamic properties and stability for the heat flux equation with linear memory, Quart. Appl. Math., LI, 2 (1993), 343-362. Zbl0780.45011MR1218373DOI10.1090/qam/1218373
  15. GOLDEN, J. M., Free energy in the frequency domain: the scalar case, Quart. Appl. Math., LVIII 1 (2000), 127-150. Zbl1032.74017MR1739041DOI10.1090/qam/1739041
  16. GRAFFI, D., Sull'espressione analitica di alcune grandezze termodinamiche nei materiali con memoria, Rend. Sem. Mat. Univ. Padova, 68 (1982), 17-29. Zbl0535.73029
  17. GRAFFI, D. - FABRIZIO, M., Non unicità dell'energia libera per materiali viscoelastici, Atti Accad. Naz. Lincei, 83 (1990), 209-214. 
  18. GURTIN, M. E. - PIPKIN, A. C., A general theory of heat conduction with finite wave speeds, Arch. Rational Mech. Anal., 31 (1968), 113-126. Zbl0164.12901MR1553521DOI10.1007/BF00281373
  19. MUSKHELISHVILI, N. I., Singular Integral Equations, Noordhoff, Groningen, 1953. MR355494
  20. VOLTERRA, V., Theory of functional and of integral and integro-differential equations, Blackie Son Limited, London,1930. Zbl55.0814.01MR100765

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