The entropy principle: from continuum mechanics to hyperbolic systems of balance laws
Bollettino dell'Unione Matematica Italiana (2005)
- Volume: 8-B, Issue: 1, page 1-20
- ISSN: 0392-4041
Access Full Article
topAbstract
topHow to cite
topRuggeri, Tommaso. "The entropy principle: from continuum mechanics to hyperbolic systems of balance laws." Bollettino dell'Unione Matematica Italiana 8-B.1 (2005): 1-20. <http://eudml.org/doc/196153>.
@article{Ruggeri2005,
abstract = {We discuss the different roles of the entropy principle in modern thermodynamics. We start with the approach of rational thermodynamics in which the entropy principle becomes a selection rule for physical constitutive equations. Then we discuss the entropy principle for selecting admissible discontinuous weak solutions and to symmetrize general systems of hyperbolic balance laws. A particular attention is given on the local and global well-posedness of the relative Cauchy problem for smooth solutions. At the end we give some recent results on closure procedure for the moments theory associated to the Boltzmann equation (Extended Thermodynamics).},
author = {Ruggeri, Tommaso},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {1-20},
publisher = {Unione Matematica Italiana},
title = {The entropy principle: from continuum mechanics to hyperbolic systems of balance laws},
url = {http://eudml.org/doc/196153},
volume = {8-B},
year = {2005},
}
TY - JOUR
AU - Ruggeri, Tommaso
TI - The entropy principle: from continuum mechanics to hyperbolic systems of balance laws
JO - Bollettino dell'Unione Matematica Italiana
DA - 2005/2//
PB - Unione Matematica Italiana
VL - 8-B
IS - 1
SP - 1
EP - 20
AB - We discuss the different roles of the entropy principle in modern thermodynamics. We start with the approach of rational thermodynamics in which the entropy principle becomes a selection rule for physical constitutive equations. Then we discuss the entropy principle for selecting admissible discontinuous weak solutions and to symmetrize general systems of hyperbolic balance laws. A particular attention is given on the local and global well-posedness of the relative Cauchy problem for smooth solutions. At the end we give some recent results on closure procedure for the moments theory associated to the Boltzmann equation (Extended Thermodynamics).
LA - eng
UR - http://eudml.org/doc/196153
ER -
References
top- COLEMAN, B. D. - NOLL, W., The thermomechanics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal., 13 (1963), 167-178. Zbl0113.17802MR153153
- MÜLLER, I., On the entropy inequality, Arch. Rational Mech. Anal., 26 (1967), 118-141. Zbl0163.46701MR214336
- A. GREEN - G. KELLER - G. WARNECKE Eds., Entropy, Series in Appl. Math.Princeton University Press, Princeton (2003). Zbl1187.00001MR2035814
- LAX, P. D., Shock Waves and Entropy, Contributions to Functional Analysis, 603-634, Ed. E. A. Zarantonello, New York, Academic Press (1971). Zbl0268.35014MR393870
- FRIEDRICHS, K. O. - LAX, P. D., Systems of conservation equations with a convex extension, Proc. Nat. Acad. Sci. USA, 68 (1971), 1686-1688. Zbl0229.35061MR285799
- DAFERMOS, C., Hyperbolic Conservation Laws in Continuum Physics, Springer Verlag, Berlin (2000). Zbl1078.35001MR1763936
- LIU, T.-P., The Riemann Problem for General System of Conservation Laws, J. Differential Equations, 18 (1975), 218-234. Zbl0297.76057MR369939
- LIU, T.-P., The Admissible Solutions of Hyperbolic Conservation Laws, Memoir of AMS, 240 (1981), 78. Zbl0446.76058MR603391
- LIU, T.-P. - RUGGERI, T., Entropy Production and Admissibility of Shocks, Acta Math. Appl. Sin., Engl. Ser., 19, No. 1 (2003), 1-12. Zbl1029.35172MR2053765
- RUGGERI, T. - STRUMIA, A., Main field and convex covariant density for quasi-linear hyperbolic systems. Relativistic fluid dynamics, Ann. Inst. Henri Poincarè, 34-A (1981), 65-84. Zbl0473.76126MR605357
- BOILLAT, G., Sur l'Existence et la Recherche d'Équations de Conservation Supplémentaires pour les Systèmes Hyperboliques, C.R. Acad. Sc. Paris, 278-A (1974), 909-912. Non Linear Fields and Waves. In CIME Course, Recent Mathematical Methods in Nonlinear Wave Propagation, Lecture Notes in Mathematics1640, T. Ruggeri Ed. Springer-Verlag (1995), 103-152. Zbl0279.35058MR342870
- GODUNOV, S. K., An interesting class of quasilinear systems, Sov. Math., Dokl.2 (1961), 947-949; translation from Dokl. Akad. Nauk SSSR, 139 (1961), 521-523. Zbl0125.06002MR131653
- BOILLAT, G. - RUGGERI, T., Hyperbolic Principal Subsystems: Entropy Convexity and Sub characteristic Conditions, Arch. Rat. Mech. Anal., 137 (1997), 305- 320. Zbl0878.35070MR1463797
- BOILLAT, G. - RUGGERI, T., On the shock structure problem for hyperbolic system of balance laws and convex entropy, Contin. Mech. Thermodyn., 10, No. 5 (1998), 285-292. Zbl0922.76237MR1652858
- 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, B. Albers editor WIAS-Report No. 18 (2000).
- RUGGERI, T. - SERRE, D., Stability of constant equilibrium state for dissipative balance laws system with a convex entropy, Quarterly of Applied Math. To appear (2003). Zbl1068.35067MR2032577
- KAWASHIMA, S., Large-time behavior of solutions to hyperbolic-parabolic systems of conservation laws and applications, Proc. R. Soc. Edinb., Sect. A, 106 (1987), 169-194. Zbl0653.35066MR899951
- FISCHER, A. E. - MARSDEN, J. E., The Einstein evolution equations as a first-order quasi-linear symmetric hyperbolic system, Commun. Math. Phys., 28 (1972), 1-38. Zbl0247.35082MR309507
- MAJDA, A., Compressible fluid flow and systems of conservation laws in several space variables, Springer Verlag, New York (1984). Zbl0537.76001MR748308
- ZENG, Y., Gas dynamics in thermal nonequilibrium and general hyperbolic systems with relaxation, Arch. Ration. Mech. Anal., 150, No. 3 (1999), 225-279. Zbl0966.76079MR1738119
- HANOUZET, B. - NATALINI, R., Global existence of smooth solutions for partially dissipative hyperbolic systems with a convex entropy, Arch. Rat. Mech. Anal., 169 (2003), 89-117. Zbl1037.35041MR2005637
- MÜLLER, I. - RUGGERI, T., Rational Extended Thermodynamics, 2nd ed., Springer Tracts in Natural Philosophy37, Springer-Verlag, New York (1998). Zbl0895.00005MR1632151
- GRAD, H., On the kinetic theory of rarefied gases, Comm. Appl. Math., 2 (1949), 331-407. Zbl0037.13104MR33674
- BOILLAT, G. - RUGGERI, T., Moment equations in the kinetic theory of gases and wave velocities, Contin. Mech. Thermodyn., 9, No. 4 (1997), 205-212. Zbl0892.76075MR1467331
- BOILLAT, G. - RUGGERI, T., Maximum wave velocity in the moments system of a relativistic gas, Contin. Mech. Thermodyn., 11, No. 2 (1999), 107-111. Zbl0935.76077MR1680244
- BOILLAT, G. - RUGGERI, T., Relativistic gas: Moment equations and maximum wave velocity, J. Math. Phys., 40, No. 12 (1999), 6399-6406. Zbl0962.82060MR1725865
- BRINI, F. - RUGGERI, T., Maximum velocity for wave propagation in a relativistic rarefied gas, Contin. Mech. Thermodyn., 11, No. 5 (1999), 331-338. Zbl0946.76084MR1723707
- WEISS, W., Die Berechnung von kontinuierlichen Stoßstrukturen in der Kinetischen Gastheorie, Habilitation thesis TU Berlin (1997).
- WEISS, W. - MÜLLER, I., Light scattering and extended thermodynamics, Cont. Mech. Thermodyn., 7 (1995), 123-144. MR1333703
- STRUCHTRUP, H., An extended moment method in radiative transfer: The matrices of mean absorption and scattering coefficients, Annals of Physics, 257, No. 2 (1997), 111-135. Zbl0937.76065MR1460874
- KREMER, G. M. - MÜLLER, I., Thermal conductivity and dynamic pressure in extended thermodynamics of chemically reacting mixtures of gases, Ann. Inst. Henri Poincaré, Phys. Théor., 69, No. 3 (1998), 309-334. Zbl0964.80007MR1648986
- ANILE, A. M. - ROMANO, V. - RUSSO, G., Extended hydrodynamical model of carrier transport in semiconductors, SIAM J. Appl. Math., 61, No. 1 (2000), 74-101. Zbl0966.35076MR1776388
- DREYER, W., Maximisation of the Entropy in Non-Equilibrium, J. Phys. A: Math. Gen., 20 (1987), 6505-6512. Zbl0633.76081MR926398
- RUGGERI, T., Breakdown of Shock Wave Structure Solutions, Phys. Rev., 47-E, (6) (1993), 4135-4140. MR1377905
- WEISS, W., Continuous shock structure in extended thermodynamics, Phys. Review E, Part A, 52 (1995), 5760-5768.
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.