Existence and uniqueness theorems for viscous fluids capable of heat conduction in a relativistic theory of non stationary thermodynamics

Franco Cardin

Annales de l'I.H.P. Physique théorique (1984)

  • Volume: 41, Issue: 2, page 171-189
  • ISSN: 0246-0211

How to cite

top

Cardin, Franco. "Existence and uniqueness theorems for viscous fluids capable of heat conduction in a relativistic theory of non stationary thermodynamics." Annales de l'I.H.P. Physique théorique 41.2 (1984): 171-189. <http://eudml.org/doc/76255>.

@article{Cardin1984,
author = {Cardin, Franco},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {existence and uniqueness theorems; relativistic continuum mechanics; hyperbolization method; conservative system of partial differential equations; Clausius-Duhem thermodynamical inequality; relativistic viscous heat conducting fluids; well-posedness},
language = {eng},
number = {2},
pages = {171-189},
publisher = {Gauthier-Villars},
title = {Existence and uniqueness theorems for viscous fluids capable of heat conduction in a relativistic theory of non stationary thermodynamics},
url = {http://eudml.org/doc/76255},
volume = {41},
year = {1984},
}

TY - JOUR
AU - Cardin, Franco
TI - Existence and uniqueness theorems for viscous fluids capable of heat conduction in a relativistic theory of non stationary thermodynamics
JO - Annales de l'I.H.P. Physique théorique
PY - 1984
PB - Gauthier-Villars
VL - 41
IS - 2
SP - 171
EP - 189
LA - eng
KW - existence and uniqueness theorems; relativistic continuum mechanics; hyperbolization method; conservative system of partial differential equations; Clausius-Duhem thermodynamical inequality; relativistic viscous heat conducting fluids; well-posedness
UR - http://eudml.org/doc/76255
ER -

References

top
  1. [1] T. Alts and I. Müller, Relativistic Thermodynamics of Simple Heat Conducting Fluids. Arch. Rat. Mech. Anal., t. 48, 1972, p. 245. Zbl0252.76083MR413788
  2. [2] M. Berger and M. Berger, Perspectives in nonlinearity. W. A. Benjamin, Inc. New York, 1968. Zbl0185.22102
  3. [3] 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. Zbl0279.35058MR342870
  4. [4] G. Boillat and T. Ruggeri, Limite de la vitesse de chocs dans les champs à densité d'énergie convex. C. R. Acad. Sci. Paris, t. 289 A, 1979, p. 257. Zbl0417.73027MR552226
  5. [5] G. Boillat and T. Ruggeri, Symmetric form of nonlinear mechanics equations and entropy growth across a shock. Acta Mechanica, t. 35, 1980, p. 271. Zbl0474.73037
  6. [6] A. Bressan, Relativistic Theories of Materials, Springer-Verlag, Berlin, Heidelberg, New York, 1978. Zbl0373.73001MR509212
  7. [7] A. Bressan, On Relativistic Heat Conduction in the Stationary and Nonstationary Cases, the Objectivity Principle and Piezo-elasticity. Lett. Al Nuovo Cimento, t. 33, n° 4, 1982, p. 108. Addendum On Relativistic Heat Conduction...Lett. Al Nuovo Cimento, t. 34, p. 63. 
  8. [8] A. Bressan, On the Relativistic Nonstationary Law of Heat Conduction and the Objectivity Principle, Piezoelasticity. Being printed on B.U.M.I. (Bollettino dell' Unione Matematica Italiana). Zbl0531.73001
  9. [9] B.D. Coleman and W. Noll, The Thermodynamics of Elastic Materials with Heat Conduction and Viscosity. Arch. Rat. Mech. Anal., t. 13, 1963, p. 167. Zbl0113.17802MR153153
  10. [10] A.E. Fisher and J.E. Marsden, The Einstein Evolution Equations as a First-Order Quasi-Linear Symmetric Hyperbolic System, I. Commun. math. Phys., t. 28, 1972, p. 1. Zbl0247.35082MR309507
  11. [11] A.E. Fisher and J.E. Marsden, General Relativity, Partial Differential Equations and Dynamical System, Proc. Symp. Pure Math., t. 23, Ed. by C. Spencer, 1973. Zbl0262.35035MR407886
  12. [12] K.O. Friedrichs, Conservation Equations and the Laws of Motion in Classical Physics. Comm. Pure Appl. Math., t. 31, 1978, p. 123. Zbl0379.35002MR509916
  13. [13] 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. Zbl0229.35061MR285799
  14. [14] S.K. Godunov, An interesting class of quasilinear systems. Sov. Math., t. 2, 1961, p. 947. Zbl0125.06002
  15. [15] E. Massa and A. Morro, A dynamical approach to relativistic continuum mechanics. Ann. Inst. Henri Poincaré, Sect. A, t. 29, 1978, p. 423. Zbl0401.73007MR525392
  16. [16] I. Müller, Towards Relativistic Thermodynamics. Arch. Rat. Mech. Anal., t. 34, 1969, p. 259. Zbl0182.59801
  17. [17] T. Ruggeri and A. Strumia, Main field and convex covariant density for quasi–linear hyperbolic systems. Relativistic Fluid Dynamics. Ann. Inst. Henri Poincaré, Sect. A, t. 34, 1981, p. 65. Zbl0473.76126MR605357
  18. [18] J. Serrin, Mathematical Principles of Classical Fluid Mechanics. Handbuch der Physik, Band VIII, Berlin-Göttingen-Heidelberg ; Springer1959. MR108116
  19. [19] C.A. Truesdell and R.A. Toupin, The Classical Field Theories. Handbuch der Physik, Band 111/1, Berlin-Göttingen-Heidelberg; Springer1960. MR118005

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.