Main field and convex covariant density for quasi-linear hyperbolic systems : relativistic fluid dynamics

Tommaso Ruggeri; Alberto Strumia

Annales de l'I.H.P. Physique théorique (1981)

  • Volume: 34, Issue: 1, page 65-84
  • ISSN: 0246-0211

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Ruggeri, Tommaso, and Strumia, Alberto. "Main field and convex covariant density for quasi-linear hyperbolic systems : relativistic fluid dynamics." Annales de l'I.H.P. Physique théorique 34.1 (1981): 65-84. <http://eudml.org/doc/76107>.

@article{Ruggeri1981,
author = {Ruggeri, Tommaso, Strumia, Alberto},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {symmetric systems; supplementary law with convex density of energy; concave entropy; concave free enthalpy},
language = {eng},
number = {1},
pages = {65-84},
publisher = {Gauthier-Villars},
title = {Main field and convex covariant density for quasi-linear hyperbolic systems : relativistic fluid dynamics},
url = {http://eudml.org/doc/76107},
volume = {34},
year = {1981},
}

TY - JOUR
AU - Ruggeri, Tommaso
AU - Strumia, Alberto
TI - Main field and convex covariant density for quasi-linear hyperbolic systems : relativistic fluid dynamics
JO - Annales de l'I.H.P. Physique théorique
PY - 1981
PB - Gauthier-Villars
VL - 34
IS - 1
SP - 65
EP - 84
LA - eng
KW - symmetric systems; supplementary law with convex density of energy; concave entropy; concave free enthalpy
UR - http://eudml.org/doc/76107
ER -

References

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  1. [1] K.O. Friedrichs, On the laws of relativistic electro-magneto-fluid dynamics. Comm. Pure Appl. Math., 1974, t. 27, p. 749-808; Conservation equations and the laws of motion in classical physics. Comm. Pure Appl. Math., t. 31, 1978, p. 123-131. Zbl0308.76075MR509916
  2. [2] A. Fisher and D.P. Marsden, The Einstein evolution equations as a first order quasilinear symmetric hyperbolic system I. Comm. Math. Phys., t. 28, 1972, p. 1-38. General relativity, partial differential equations and dynamical systems. Proc. Symp. Pure Math., t. 23, Ed. by C. Spencer; Amer. Math. Soc., 1973. MR309507
  3. [3] K.O. Friedrichs and P.D. Lax, Systems of conservation equations with a convex extension. Proc. Nat. Acad. Sci. U. S. A., t. 68, 1971, p. 1686-1688. Zbl0229.35061MR285799
  4. [4] P.D. Lax, Shock waves and entropy in: Contributions to non linear functional analysis (ed. E. H. Zarantonello), New York; Academic Press, 1971, p. 603-634. Zbl0268.35014MR393870
  5. [5] G. Boillat, Sur une fonction croissante comme l'entropie et génératrice des chocs dans les systèmes hyperboliques. C. R. Acad. Sci., Paris, t. 283 A, 1976, p. 409-412. Zbl0336.35071MR421293
  6. [6] G. Boillat and T. Ruggeri, Limite de la vitesse des chocs dans les champs à densité d'énergie convex. C. R. Acad. Sci., t. 289 A, 1979, p. 257-258. Zbl0417.73027MR552226
  7. [7] M. Berger and M. Berger, Perspectives in nonlinearity. W. A. Benjamin, Inc. New York, 1968, p. 137. Zbl0185.22102
  8. [8] S.K. Godunov, An interesting class of quasilinear systems. Sov. Math., t. 2, 1961, p. 947-948. Zbl0125.06002MR116141
  9. [9] G. Boillat, Sur l'existence et la recherche d'équations de conservation supplémentaires pour les systèmes hyperboliques. C. R. Acad. Sci., Paris, t. 278 A, 1974, p. 909-912. Zbl0279.35058MR342870
  10. [10] G. Boillat and T. Ruggeri, Symmetric form of nonlinear mechanics equations and entropy growth across a shock. Acta Mechanica, t. 35, 1980, p. 271-274. Zbl0474.73037
  11. [11] D. Fusco, Alcune considerazioni sulle onde d'urto in fluidodinamica. Rend. Sem. Mat. di Modena, t. 28, 1979, 223-233. Zbl0435.76042
  12. [12] I.- Shih Liu, Method of Lagrange Multipliers for exploitation of the entropy principle. Arch. Rat. Mech. Anal., t. 46, 1972, p. 131-148. Zbl0252.76003MR337164
  13. [13] I. Müller, The coldness, a universal function in thermoelastic bodies, Arch. Rat. Mech. Anal., t. 41, 1971, p. 319-332. Entropy in non-equilibrium—a challenge to mathematicians. Trend in Application of Pure Mathematics to Mechanics, Vol. II, Ed. H. Zorski, PitmanLondon, 1979, p. 281-295. Zbl0225.73003MR345531
  14. [14] S.N. Kruskov, Results on the character of continuity of solutions of parabolic equations and some their applications. Math. Zametky, t. 6, 1969; p. 97-108. 
  15. [15] E. Hopf, On the right weak solution of the Cauchy problem for quasilinear equation of first order. J. of Math. and Mech., t. 19, 1969, p. 487-493. Zbl0188.16102MR251357
  16. [16] A. Lichnerowicz, Ondes des choc, ondes infinitésimales et rayons en hydrodynamique et magnétohydrodynamique relativistes, in: Relativistic fluid dynamics, Corso CIME1970, 87-203 Ed. Cremonese, 1971. Shock waves in relativistic magnetohydrodynamics under general assumptions. Journal of Math. Phys., t. 17, 1976, p. 2135-2142. Relativistic Hydrodynamics and Magnetohydrodynamics, W. A. Benjamin, New York, 1967. MR297295
  17. [17] L. Landau and E. Lifchtiz, Mécanique des fluides, ed. MIR, Moscou, 1971, p. 625. Zbl0216.25801
  18. [18] D. Ter Haar and H. Wergeland, Elements of thermodynamics. Addison Wesley Publ. Co., Reading, Mass., 1966. 

Citations in EuDML Documents

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  1. A. M. Anile, S. Pennisi, M. Sammartino, Covariant radiation hydrodynamics
  2. Alberto Strumia, Some remarks on conservative symmetric-hyperbolic systems governing relativistic theories
  3. Franco Cardin, Existence and uniqueness theorems for viscous fluids capable of heat conduction in a relativistic theory of non stationary thermodynamics
  4. Carmela Currò, Domenico Fusco, Discontinuous travelling wave solutions for a class of dissipative hyperbolic models
  5. Ingo Müller, Extended thermodynamics---a theory of symmetric hyperbolic field equations
  6. Giovanni Mascali, Vittorio Romano, Maximum entropy principle in relativistic radiation hydrodynamics
  7. A. M. Blokhin, V. Romano, Yu. L. Trakhinin, Stability of shock waves in relativistic radiation hydrodynamics
  8. Tommaso Ruggeri, The entropy principle: from continuum mechanics to hyperbolic systems of balance laws
  9. Sebastiano Pennisi, A covariant and extended model for relativistic magnetofluiddynamics

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