Entropy principle and relativistic extended thermodynamics: Global existence of smooth solutions and stability of equilibrium state

Nuovo Cimento della Societa Italiana di Fisica B

Volumn 119, Issue 7-9, 2004, Pages 809-821

  Ruggeri, T ^a  

^a UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 17744385544     PISSN: 15949982     EISSN: None     Source Type: Journal    
DOI: 10.1393/ncb/i2004-10207-6     Document Type: Article

References (25)

1. DAFERMOS C., Hyperbolic Conservation Laws in Continuum Physics (Springer Verlag, Berlin) 2000.
2. RUGGERI T., The Entropy Principle: from Continuum Mechanics to Hyperbolic Systems of Balance Laws, to be published in Bollettino Unione Matematica Italiana (2004).
3. BOILLAT G., Sur l'existence et la recherche d'équations de conservation supplémentaires pour les Systèmes Hyperboliques, C. R. Acad. Sci. Paris A, 278 (1974) 909; Non-linear fields and waves, in CIME Course, Recent Mathematical Methods in Nonlinear Wave Propagation, edited by RUGGERI T., Lect. Notes Math., Vol. 1640 (Springer-Ver lag) 1995, pp. 103-152.
4. BOILLAT G., Sur l'existence et la recherche d'équations de conservation supplémentaires pour les Systèmes Hyperboliques, C. R. Acad. Sci. Paris A, 278 (1974) 909; Non-linear fields and waves, in CIME Course, Recent Mathematical Methods in Nonlinear Wave Propagation, edited by RUGGERI T., Lect. Notes Math., Vol. 1640 (Springer-Ver lag) 1995, pp. 103-152.
5. RUGGERI T. and STRUMIA A., Main field and convex covariant density for quasi-linear hyperbolic systems. Relativistic fluid dynamics, Ann. Inst. Henri Poincare A, 34 (1981) 65.
6. BOILLAT G. and RUGGERI T., Hyperbolic Principal Subsystems: Entropy Convexity and Sub characteristic Conditions, Arch. Ration. Mech. Anal., 137 (1997) 305.
7. FRIEDRICHS K. O. and LAX P. D., Systems of conservation equations with a convex extension, Proc. Nat. Acad. 3d. USA, 68 (1971) 1686.
8. GODUNOV S. K., An interesting class of quasilinear systems, Sov. Math., 2 (1961) 947.
9. BOILLAT G. and RUGGERI T., On the shock structure problem for hyperbolic system of balance laws and convex entropy, Cont. Mech. Thermodyn., 10 (1998) 285.
10. RUGGERI T., Maximum of Entropy Density in Equilibrium and Minimax Principle for an Hyperbolic System of Balance Laws. Contributions to Continuum Theories, Anniversary Volume for Krzysztoff Wilmanski, edited by ALBERS B., WIAS-Report No. 18 (2000).
11. RUGGERI T. and SERRE D., Stability of constant equilibrium state for dissipative balance laws system with a convex entropy, Q. Appl. Math., 62 (2003) 163.
12. KAWASHIMA S., Large-time behavior of solutions to hyperbolic-parabolic systems of conservation laws and applications, Proc. R. Soc. Edinburgh A, 106 (1987) 169.
13. FISCHER A. E. and MARSDEN J. E., The Einstein evolution equations as a first-order quasi-linear symmetric hyperbolic system, Commun. Math. Phys., 28 (1972) 1.
14. MAJDA A., Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables (Springer Verlag, NewYork) 1984.
15. ZENG Y., Gas dynamics in thermal nonequilibrium and general hyperbolic systems with relaxation, Arch. Ration. Mech. Anal., 150 (1999) 225.
16. HANOUZET B. and NATALINI R., Global existence of smooth solutions for partially dissipative hyperbolic systems with a convex entropy, Arch. Ration. Mech. Anal., 169 (2003) 89.
17. WEN AN YONG, Entropy and Global Existence for Hyperbolic Balance Laws, Arch. Ration. Mech. Anal., 172 (2004) 247.
18. RUGGERI T., Global existence of smooth solutions and stability of constant state for dissipative Hyperbolic Systems with applications to the Extended Thermodynamics, Lect. Notes of STAMM 2002 (Springer-Verlag) 2004.
19. RUGGERI T., Some recent mathematical results in mixtures theory of Euler fluids, in Proceedings WASCOM 2003, edited by MONACO R., PENNISI S., RIONERO S. and RUGGERI T. (World Scientific, Singapore) pp. 441-454. RUGGERI T., Global Existence, Stability and Non Linear Wave Propagation in Binary Mixtures, Convegno in onore di S. Rionero, Napoli 2003 (World Scientific) 2004.
20. RUGGERI T., Some recent mathematical results in mixtures theory of Euler fluids, in Proceedings WASCOM 2003, edited by MONACO R., PENNISI S., RIONERO S. and RUGGERI T. (World Scientific, Singapore) pp. 441-454. RUGGERI T., Global Existence, Stability and Non Linear Wave Propagation in Binary Mixtures, Convegno in onore di S. Rionero, Napoli 2003 (World Scientific) 2004.
21. MÜLLER I. and RUGGERI T., Rational Extended Thermodynamics, 2nd edition, Springer Tracts Nat. Philos., Vol. 37 (Springer-Verlag, New York) 1998.
22. BOILLAT G. and RUGGERI T., Relativistic gas: Moment equations and maximum wave velocity, J. Math. Phys., 40 (1999) 6399.
23. SHIH LIU I., MÜLLER I., RUGGERI T., Relativistic thermodynamics of gases, Ann. Phys. (N.Y.), 169 (1986) 191.
24. MÜLLER I. and RUGGERI T., Rational Extended Thermodynamics, 1st edition, Springer Tracts Nat. Philos., Vol. 37 (Springer-Verlag, New York) 1993.
25. SECCIA L. and STRUMIA A., Wave propagation in relativistic extended thermodynamics, Cont. Mech. Thermodyn., 2 (1990) 151.