On the causality requirement for diffusive-hyperbolic systems in non-equilibrium thermodynamics

Journal of Non-Equilibrium Thermodynamics

Volumn 29, Issue 2, 2004, Pages 125-139

  Cimmelli, V A ^a  

^a UNIVERSITY OF BASILICATA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

HEAT CONDUCTION; KINETIC THEORY; PARAMETER ESTIMATION; SUPERCONDUCTIVITY; VISCOSITY; WAVE PROPAGATION;

CLASSICAL NEWTONIAN MECHANICS; DIFFUSIVE-HYPERBOLIC SYSTEMS; NON-EQUILIBRIUM THERMODYNAMICS;

THERMODYNAMICS;

EID: 3042646565     PISSN: 03400204     EISSN: None     Source Type: Journal    
DOI: 10.1515/JNETDY.2004.008     Document Type: Article

References (34)

1. Müller, I., Ruggeri, T., Rational Extended Thermodynamics, Springer-Verlag, Berlin, 1998.
2. Jou, D., Casas-Vasquez, J., Lebon, J., Extended Irreversible Thermodynamics, Springer-Verlag, Berlin, 1996.
3. Jou, D., Casas-Vasquez, J., Extended irreversible thermodynamics and its relation with other continuum approaches, J. Non-Newtonian Fluid Mech., 96 (2001), 77-104.
4. Truesdell, C., Rational Thermodynamics, 2nd ed., Springer Verlag, Berlin, 1984.
5. Fichera, G., Is the Fourier theory of heat propagation paradoxical?, Rendiconti del Circolo Matematico di Palermo, Serie II, Tomo XLI (1992), 5-16.
6. Day, W.A., A note on the propagation of temperature disturbances, Quart. Appl. Math., 55 (1997), 565-572.
7. Day, W.A., Two lines of defense of Fourier's theory of heat propagation, in: Homage to Gaetano Fichera, Ed. A. Cialdea, pp. 147-159, Aracne, Rome, 2000.
8. Jackson, H.E., Walker, C.T., Thermal conductivity, second sound, and phonon-phonon interactions in NaF, Phys. Rev. Lett., 3 (1971), 1428-1439.
9. Narayanamurti, V., Dynes, R.C., Observation of second sound in Bismuth, Phys. Rev. Lett., 28 (1972), 1461-1465.
10. Dafermos, C.M., Hyperbolic Conservation Laws in Continuum Physics, Springer Verlag, Berlin, 2000.
11. Smoller, J., Shock Waves and Reaction-Diffusion Equations, Springer Verlag, Berlin, 1983.
12. Muschik, W., Papenfuss, C., Ehrentraut, H., A sketch of continuum thermodynamics, J. Non-Newtonian Fluid Mech., 96 (2001), 255-290.
13. Cimmelli, V.A., Kosiński, W., Nonequilibrium semi-empirical temperature in materials with thermal relaxation, Arch. Mech., 43 (1991), 753-767.
14. Kosiński, W., Wojno, W., Gradient generalization to internal state variable approach, Arch. Mech., 47 (1995), 523-536.
15. Kosiński, W., Wojno, W., On parabolic regularization of hyperbolic heat conductivity in rigid body, J. Theor. Appl. Mech., 1 (1996), 67-76.
16. Liu, I-Shih, Method of Lagrange multipliers for exploitation of the entropy principle, Arch. Rat. Mech. Anal., 46 (1972), 131-148.
17. Cattaneo, C., Sulla conduzione del calore, Atti Sem. Mat. Fis. Univ. Modena, 3 (1948), 83-101.
18. Caccese, E., Cimmelli, V.A., Pace, A.R., On a general definition for inertial theories of space and time, Hadronic J., 24 (2001), 345-384.
19. Dixon, W.G., Special Relativity: The Foundation of Macroscopic Physics, Cambridge University Press, Cambridge, 1978.
20. Boillat, G., La Propagation des Ondes, Gauthier-Villars, Paris, 1965.
21. Israel, W., Nonstationary Irreversible Thermodynamics: A Causal Relativistic Theory, Ann. Phys., 100 (1976), 341-372.
22. Joseph, D.D., Preziosi, L., Heat Waves, Rev. Mod. Phys., 61 (1989), 41-73. Addendum, Rev. Mod. Phys., 62 (1990), 375-391.
23. Joseph, D.D., Preziosi, L., Heat Waves, Rev. Mod. Phys., 61 (1989), 41-73. Addendum, Rev. Mod. Phys., 62 (1990), 375-391.
24. Chandrasekharaiah, D.S., Hyperbolic thermoelasticity: A review of recent literature, Appl. Mech. Rev., 51 (1998), 705-729.
25. Casas-Vásquez, J., Jou, D., Temperature in non-equilibrium states: A review of open problems and current proposals, Rep. Prog. Phys., 66 (2003), 1937-2023.
26. Frischmuth, K., Cimmelli, V.A., Numerical reconstruction of heat pulse experiments, Int. J. Engng. Sci., 33 (1994), 209-215.
27. Cimmelli, V.A., Frischmuth, K., Determination of material functions through second sound measurements in a hyperbolic heat conduction theory, Math. Comput. Modelling, 24 (1996), 19-28.
28. Verhás, J., Thermodynamics and Rheology, Kluwer Academic Publisher, Dordrecht, 1997.
29. Müller, I., A thermodynamic theory of mixtures of fluids, Arch. Rat. Mech. Anal., 28 (1968), 1-39.
30. Maugin, G.A., Internal variables and dissipative structures, J. Non-Equilib. Thermodyn., 15 (1990), 173-192.
31. Kirchner, N.P., Hauser, R.A., A historical note on the entropy principle of Müller and Liu, Continuum Mech. Thermodyn. 14 (2002), 223-226.
32. Van, P., Weakly nonlocal irreversible thermodynamics, Ann. Phys., 12 (2003), 142-169.
33. Coleman, B.D., Owen, D.R., A mathematical foundation for thermodynamics, Arch. Rat. Mech. Anal., 54 (1974), 1-104.
34. Coleman, B.D., Neumann, D.C., Implication of a nonlinearity in the theory of second sound in solids, Phys. Rev. B, 37 (1988), 1492-1498.