On a supplementary conservation law for a hyperbolic model of heat conductor

Mariano Torrisi; Antonino Valenti

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1990)

  • Volume: 1, Issue: 2, page 171-176
  • ISSN: 1120-6330

Abstract

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In the context of the wave propagation theory in nonlinear hyperbolic systems, we analyse, in the case of a rigid heat conductor, the model proposed by G. Grioli. After introducing the constitutive relations according to the point of view of the extended thermodynamics, we look for the compatibility of the governing equations with a supplementary conservation law. We obtain the functional form of the constitutive quantities and we are able to show that the governing equations may be written in symmetric and conservative form so that the Cauchy problem results well posed.

How to cite

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Torrisi, Mariano, and Valenti, Antonino. "On a supplementary conservation law for a hyperbolic model of heat conductor." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 1.2 (1990): 171-176. <http://eudml.org/doc/244305>.

@article{Torrisi1990,
abstract = {In the context of the wave propagation theory in nonlinear hyperbolic systems, we analyse, in the case of a rigid heat conductor, the model proposed by G. Grioli. After introducing the constitutive relations according to the point of view of the extended thermodynamics, we look for the compatibility of the governing equations with a supplementary conservation law. We obtain the functional form of the constitutive quantities and we are able to show that the governing equations may be written in symmetric and conservative form so that the Cauchy problem results well posed.},
author = {Torrisi, Mariano, Valenti, Antonino},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Thermodynamics; Hyperbolic systems; Convexity; entropy principle},
language = {eng},
month = {5},
number = {2},
pages = {171-176},
publisher = {Accademia Nazionale dei Lincei},
title = {On a supplementary conservation law for a hyperbolic model of heat conductor},
url = {http://eudml.org/doc/244305},
volume = {1},
year = {1990},
}

TY - JOUR
AU - Torrisi, Mariano
AU - Valenti, Antonino
TI - On a supplementary conservation law for a hyperbolic model of heat conductor
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1990/5//
PB - Accademia Nazionale dei Lincei
VL - 1
IS - 2
SP - 171
EP - 176
AB - In the context of the wave propagation theory in nonlinear hyperbolic systems, we analyse, in the case of a rigid heat conductor, the model proposed by G. Grioli. After introducing the constitutive relations according to the point of view of the extended thermodynamics, we look for the compatibility of the governing equations with a supplementary conservation law. We obtain the functional form of the constitutive quantities and we are able to show that the governing equations may be written in symmetric and conservative form so that the Cauchy problem results well posed.
LA - eng
KW - Thermodynamics; Hyperbolic systems; Convexity; entropy principle
UR - http://eudml.org/doc/244305
ER -

References

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  1. HUTTER, K., The foundations of Thermodynamics, its basic postulates and implications. A review of modern thermodynamics.. Acta Mech., 27, 1977, 1-54. MR502984
  2. MORRÒ, A. - RUGGERI, T., Propagazione del calore ed equazioni costitutive. Quaderno CNR, Pitagora, Bologna1984, 54. 
  3. JOU, D. - CASAS-VAZQUEZ, J. - LEBON, G., Extended irreversible thermodynamics. Rep. Prog. Phys., 51, 1988, 1105-1179. Zbl0785.73002MR959296
  4. GRIOLI, G., Sulla propagazione di onde termomeccaniche nei continui. Nota I. Atti Acc. Lincei Rend. fis., s. 8, vol. 67, 1979, 332-339. Zbl0446.73098
  5. GRIOLI, G., Sulla propagazione di onde termomeccaniche nei continui. Nota II. Atti Acc. Lincei Rend. fis., s. 8, vol. 67, 1979, 426-432. Zbl0463.73148
  6. MAXWELL, J. C., On the dynamical theory of gases. Phil. Trans. Roy. Soc., 157, London 1967, 49-88. JFM01.0379.01
  7. CATTANEO, C., Sulla conduzione del calore. Atti del Seminario matematico e fisico dell'Università di Modena, 3, 1948, 83-101. Zbl0035.26203MR32898
  8. GRIOLI, G., Questioni di termodinamica estesa. Atti Acc. Gioenia di Catania, 1987. 
  9. MULLER, I., The coldness, an universal function in thermoelastic bodies. Arch. Rat. Mech. Analysis, 41, 1971, 319-332. Zbl0225.73003MR345531
  10. FRIEDRICHS, K. O. - LAX, P. D., Systems of conversation equations with a convex extension. Proc. Nat. Sc. USA, 68, 1971, 1686-1688. Zbl0229.35061MR285799
  11. SHIH LIU, I., Method of Lagrange multipliers for exploitation of the entropy principle. Arch. Rat. Mech. Analysis, 46, 1972, 131-148. Zbl0252.76003MR337164
  12. BOILLAT, G., Sur l'existence et la recherche d'équations de conservation supplémentaires pour les systems hyperboliques. C. R. Acad. Sc. Paris, 270A, 1974, 909-912. Zbl0279.35058MR342870
  13. FISHER, A. - MARSDEN, D. P., The Einstein evolution equations as a first order quasilinear symmetric hyperbolic system. Comm. Math. Phys., 28, 1972, 1-38. Zbl0247.35082MR309507
  14. LAX, P. D., Shock waves and entropy. In: E. H. ZARANTONELLO (éd.), Contributions to non-linear functional analysis. Academic Press, New York1971. Zbl0268.35014MR367471
  15. BOILLAT, G., Sur une function croissante comme l'entropie et génératrice des chocs dans les systèmes hyperboliques. C.R. Acad. Sc. Paris, 238A, 1976, 409-412. Zbl0336.35071MR421293
  16. BOILLAT, G., Urti. In: G. FERRARESE (éd.), The wave propagation. (CIME 1980)Liguori, Napoli1982, 167-192. Zbl1230.76006
  17. RUGGERI, T., «Entropy principle» and main field for a nonlinear covariant system. In: G. FERRARESE (ed.), The wave propagation. (CIME 1980)Liguori, Napoli1982, 257-273. 
  18. TORRISI, M., Su una legge di conservazione supplementare per un modello per la conduzione del calore in un conduttore rigido. Atti Acc. Peloritana dei Pericolanti, 63, 1987, 181-189. Zbl0636.73100
  19. FRANCHI, F., Wave propagation in heat conducting dielectric solids with thermal relaxation and temperature dependent electric permettivity. Riv. Mat. Univ. Parma, 11, 1985, 443-461. Zbl0606.73117MR851554
  20. COLEMAN, B. D. - HRUSA, W. J. - OWEN, D. R., Stability of equilibrium for a nonlinear hyperbolic system describing heat propagation by second sound in solids. Arch. Ration. Mech. Anal., 94, 1986, 267-289. Zbl0621.73132MR846065DOI10.1007/BF00279867
  21. BAMPI, F. - FUSCO, D., Nonlinear wave analysis of hyperbolic model for heat conduction. Atti Sem. Fis. Modena, 36, 1988, 197-209. Zbl0664.73003MR956789
  22. MURACCHINI, A. - RUGGERI, T., Problema magnetoelasticità nonlineare di Cauchy e forma simmetrica per le equazioni della magnetoelasticità nonlineare. Atti Sem. Mat. Fis. Modena, 37, 1989, 183-193. Zbl0674.73075MR994064

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