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1. | CMAP, CNRS, Ecole Polytechnique, 91128 Palaiseau cedex, France |
2. | ONERA, Centre de Palaiseau, 91198 Palaiseau cedex, France |
References:
[1] |
R. Aris, Prolegomena to the rational analysis of systems of chemical reactions, Archiv. Rat. Mech. Anal., 19 (1965), 81-99. |
[2] |
R. J. Bearman and J. G. Kirkwood, The statistical mechanics of transport processes. XI. Equations of transport in multicomponent systems, J. Chem. Phys., 28 (1958), 136-145. |
[3] |
H. Van Beijeren and M. H. Ernst, The modified enskog equations, Phys. A, 68 (1973), 437-456. |
[4] |
H. Van Beijeren and M. H. Ernst, The modified enskog equations for mixtures, Phys. A, 70 (1973), 225-242. |
[5] |
R. Bendahklia, V. Giovangigli and D. Rosner, Soret effects in laminar counterflow spray diffusion flames, Comb. Theory Mod., 6 (2002), 1-17. |
[6] |
G. Billet, V. Giovangigli and G. de Gassowski, Impact of volume viscosity on a shock-hydrogen bubble interaction, Comb. Theory Mod., 12 (2008), 221-248.
doi: 10.1080/13647830701545875. |
[7] |
D. Bresch and B. Desjardins, On the existence of global weak solutions to the Navier-Stokes equations for viscous compressible and heat conducting fluids, J. Math. Pure Appl., 87 (2007), 57-90.
doi: 10.1016/j.matpur.2006.11.001. |
[8] |
S. Chapman and T. G. Cowling, "The Mathematical Theory of Non-Uniform Gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases," Third edition, prepared in co-operation with D. Burnett, Cambridge University Press, London, 1970. |
[9] |
G. Q. Chen, C. D. Levermore and T.-P. Liu, Hyperbolic conservation laws with stiff relaxation terms and entropy, Comm. Pure Appl. Math., 47 (1994), 787-830.
doi: 10.1002/cpa.3160470602. |
[10] |
J.-P. Croisille and P. Delorme, Kinetic symmetrizations and pressure laws for the Euler equations, Physica D, 57 (1992), 395-416.
doi: 10.1016/0167-2789(92)90010-K. |
[11] |
C. Dafermos, "Hyperbolic Conservation Laws in Continuum Physics," Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 325, Springer-Verlag, Berlin, 2000.
doi: 10.1007/3-540-29089-3_14. |
[12] |
P. Degond, S. Genieys and A. Jüengel, A system of parabolic equations in nonequilibrium thermodynamics including thermal and electric effects, J. Math. Pure Appl., 160 (1997), 991-1015. |
[13] |
S. R. de Groot and P. Mazur, "Non-Equilibrium Thermodynamics," Dover publications, Inc., New York, 1984. |
[14] |
A. Ern and V. Giovangigli, Thermal diffusion effects in hydrogen-air and methane-air flames, Comb. Theory Mod., 2-4 (1998), 349-372. |
[15] |
A. Ern and V. Giovangigli, "Multicomponent Transport Algorithms," Lecture Notes in Physics, New Series m: Monographs, 24, Springer-Verlag, Berlin, 1994. |
[16] |
A. Ern and V. Giovangigli, Thermal conduction and thermal diffusion in dilute polyatomic gas mixtures, Physica A, 214 (1995), 526-546. |
[17] |
A. Ern and V. Giovangigli, Structure of transport linear systems in dilute isotropic gas mixtures, Phys. Rev. E (3), 53 (1996), 485-492.
doi: 10.1103/PhysRevE.53.485. |
[18] |
A. Ern and V. Giovangigli, Optimized transport algorithms for flame codes, Comb. Sci. Tech., 118 (1996), 387-395. |
[19] |
A. Ern and V. Giovangigli, Projected iterative algorithms with application to multicomponent transport, Linear Algebra Appl., 250 (1997), 289-315.
doi: 10.1016/0024-3795(95)00502-1. |
[20] |
A. Ern and V. Giovangigli, The Kinetic equilibrium regime, Physica A, 260 (1998), 49-72. |
[21] |
L. C. Evans, A survey of entropy methods for partial differential equations, Bulletin of the AMS (N.S.), 41 (2004), 409-438.
doi: 10.1090/S0273-0979-04-01032-8. |
[22] |
E. Feireisl, "Dynamics of Viscous Compressible Fluids," Oxford Lecture Series in Mathematics and its Applications, 26, Oxford University Press, Oxford, 2004. |
[23] |
J. H. Ferziger and H. G. Kaper, "Mathematical Theory of Transport Processes in Gases," North-Holland Publishing Company, Amsterdam, 1972. |
[24] |
K. O. Friedrichs and P. D. Lax, Systems of conservation laws with a convex extension, Proc. Nat. Acad. Sci. USA, 68 (1971), 1686-1688. |
[25] |
W. H. Furry, On the elementary explanation of diffusion phenomena in gases, Am. J. Phys., 16 (1948), 63-78. |
[26] |
V. Giovangigli, Convergent iterative methods for multicomponent diffusion, Impact Comput. Sci. Eng., 3 (1991), 244-276.
doi: 10.1016/0899-8248(91)90010-R. |
[27] |
V. Giovangigli, "Multicomponent Flow Modeling," Modeling and Simulation in Science, Engineering and Technology, Birkhäuser Boston, Inc., Boston, MA, 1999.
doi: 10.1007/978-1-4612-1580-6. |
[28] |
V. Giovangigli, Persistence of Boltzmann entropy in fluid models, Disc. Cont. Dyn. Syst., 24 (2009), 95-114.
doi: 10.3934/dcds.2009.24.95. |
[29] |
V. Giovangigli, Higher order entropies, Arch. Rat. Mech. Anal., 187 (2008), 221-285.
doi: 10.1007/s00205-007-0065-5. |
[30] |
V. Giovangigli, Higher order entropies for compressible fluid models, Math. Mod. Meth. Appl. Sci., 19 (2009), 67-125.
doi: 10.1142/S021820250900336X. |
[31] |
V. Giovangigli, Multicomponent transport algorithms for partially ionized mixtures, J. Comp. Phys., 229 (2010), 4117-4142.
doi: 10.1016/j.jcp.2010.02.001. |
[32] |
V. Giovangigli and M. Massot, Asymptotic stability of equilibrium states for multicomponent reactive flows, Math. Mod. Meth. App. Sci., 8 (1998), 251-297.
doi: 10.1142/S0218202598000123. |
[33] |
V. Giovangigli and M. Massot, Entropic structure of multicomponent reactive flows with partial equilibrium reduced chemistry, Math. Meth. Appl. Sci., 27 (2004), 739-768.
doi: 10.1002/mma.429. |
[34] |
V. Giovangigli and L. Matuszewski, Supercritical fluid thermodynamics from equations of state, Phys. D, 241 (2012), 649-670.
doi: 10.1016/j.physd.2011.12.002. |
[35] |
V. Giovangigli and L. Matuszewski, Mathematical modeling of supercritical multicomponent reactive fluids, to appear, M3AS, (2012). |
[36] |
V. Giovangigli, L. Matuszewski and F. Dupoirieux, Detailed modeling of planar transcritical $H_2$-$O_2$-$N_2$ flames, Combustion Theory and Modelling, 15 (2011), 141-182. |
[37] |
V. Giovangigli and B. Tran, Mathematical analysis of a Saint-Venant model with variable temperature, Math. Mod. Meth. Appl. Sci., 20 (2010), 1251-1297.
doi: 10.1142/S0218202510004593. |
[38] |
A. Glitzky, K. Gröger and R. Hünlich, Free energy and dissipation rate for reaction diffusion processes of electrically charged species, Appl. Anal., 60 (1996), 201-217.
doi: 10.1080/00036819608840428. |
[39] |
S. Godunov, An interesting class of quasilinear systems, Sov. Math. Dokl., 2 (1961), 947-949. |
[40] |
E. A. Guggenheim, "Thermodynamics," North Holland, Amsterdam, 1962. |
[41] |
J. O. Hirschfelder, C. F. Curtiss and R. B. Bird, "Molecular Theory of Gases and Liquids," Wiley, New York, 1954. |
[42] |
T. J. R. Hughes, L. P. Franca and M. Mallet, A new finite element formulation for computational fluid dynamics. I. Symmetric forms of the compressible Euler and Navier-Stokes equations and the second law of thermodynamics, Comp. Meth. Appl. Mech. Eng., 54 (1986), 223-234.
doi: 10.1016/0045-7825(86)90127-1. |
[43] |
J. H. Irving and J. G. Kirkwood, The statistical mechanical theory of transport processes. IV. The equations of hydrodynamics, J. Chem. Phys., 18 (1950), 817-829. |
[44] |
A. Jüengel and I. Stelzer, Existence analysis of Maxwell-Stefan systems for multicomponent mixtures, arXiv:1211.2394, (2012). |
[45] |
S. Kawashima, "Systems of a Hyperbolic-Parabolic Composite Type, with Applications to the Equations of Magnetohydrodynamics," Doctoral Thesis, Kyoto University, 1984. |
[46] |
S. Kawashima, Large-time behavior of solutions to hyperbolic-parabolic systems of conservations laws and applications, Proc. Roy. Soc. Edinburgh Sect. A, 106 (1987), 169-194.
doi: 10.1017/S0308210500018308. |
[47] |
S. Kawashima and Y. Shizuta, On the normal form of the symmetric hyperbolic-parabolic systems associated with the conservation laws, Tohoku Math. J. (2), 40 (1988), 449-464.
doi: 10.2748/tmj/1178227986. |
[48] |
S. Kawashima and W.-A. Yong, Dissipative structure and entropy for hyperbolic systems of conservation laws, Arch. Rat. Mech. Anal., 174 (2004), 345-364.
doi: 10.1007/s00205-004-0330-9. |
[49] |
J. Keizer, "Statistical Thermodynamics of Nonequilibrium Processes," Springer-Verlag, New York, 1987. |
[50] |
F. J. Krambeck, The mathematical structure of chemical kinetics in homogeneous single-phase systems, Arch. Rational Mech. Anal., 38 (1970), 317-347.
doi: 10.1007/BF00251527. |
[51] |
V. I. Kurochkin, S. F. Makarenko and G. A. Tirskii, Transport coefficients and the Onsager relations in the kinetic theroy of dense gas mixtures, J. Appl. Mech. Tech. Phys., 25 (1984), 218-225. |
[52] |
P.-L. Lions, B. Perthame and E. Tadmor, Kinetic formulation of the isentropic gas dynamics and $p$-systems, Comm. Math. Phys., 163 (1994), 415-431. |
[53] |
M. R. Marcelin, "Sur la Mécanique des Phénomènes Irréversibles," Comptes Rendus de l'Académie des Sciences de Paris, Séance du 5 décembre 1910, (1910), 1052-1055. |
[54] |
J. Meixner, Zur Thermodynamik der irreversiblen Prozesse in Gasen mit chemisch reagierenden, dissoziierenden und anregbaren Komponenten, Ann. der Phys., 43 (1943), 244-270. |
[55] |
H. Mori, Statistical-mechanical theory of transport in fluids, Phys. Rev., 112 (1958), 1829-1842. |
[56] |
I. Prigogine, "Etude Thermodynamique des Phénomènes Irréversibles," Dunod, Paris, 1947. |
[57] |
J. Pousin, "Modélisation et Analyse Numérique de Couches Limites Réactives d'Air," Doctorat es Sciences, Ecole Polytechnique Fédérale de Lausanne, 1112, 1993. |
[58] |
T. Ruggeri, Thermodynamics and Symmetric Hyperbolic Systems. Nonlinear hyperbolic equations in applied sciences,, Rend. Sem. Mat. Univ. Politec. Torino, 1988 (): 167.
|
[59] |
N. Z. Shapiro and L. S. Shapley, Mass action law and the Gibbs free energy function, SIAM J. Appl. Math., 13 (1965), 353-375. |
[60] |
D. Serre, Systèmes de Lois de Conservation. I et II, Diderot Editeur, Paris, 1996. |
[61] |
D. Serre, The structure of dissipative viscous system of conservation laws, Physica D, 239 (2010), 1381-1386.
doi: 10.1016/j.physd.2009.03.014. |
[62] |
Y. Shizuta and S. Kawashima, Systems of Equations of hyperbolic-parabolic type with applications to the discrete Boltzmann equation, Hokkaido Math. J., 14 (1985), 249-275. |
[63] |
R. Taylor and R. Krishna, "Multicomponent Mass Transfer," John Wiley, New York, 1993. |
[64] |
T. Umeda, S. Kawashima and Y. Shizuta, On the Decay of solutions to the linearized equations of electromagnetofluid dynamics, Japan J. Appl. Math., 1 (1984), 435-457.
doi: 10.1007/BF03167068. |
[65] |
J. Van de Ree, On the definition of the diffusion coefficients in reacting gases, Physica, 36 (1967), 118-126. |
[66] |
A. I. Vol'pert and S. I. Hudjaev, On the Cauchy problem for composite systems of nonlinear differential equations, Mat. Sb. (N.S.), 87(129) (1972), 504-528. |
[67] |
L. G. Vulkov, On the conservation laws of the Compressible euler equations, Applicable Analysis, 64 (1997), 255-271.
doi: 10.1080/00036819708840534. |
[68] |
L. Waldmann, Transporterscheinungen in Gasen von mittlerem Druck, in "1958 Handbuch der Physik," Bd. 12, Thermodynamik der Gase, Springer-Verlag, Berlin-Göttingen-Heidelberg, (1958), 295-514. |
[69] |
J. Wei, An axiomatic treatment of chemical reaction systems, J. Chem. Phys., 36 (1962), 1578-1584. |
[70] | |
[71] |
W.-A. Yong, Entropy and global existence for hyperbolic balance laws, Arch. Rat. Mech. Anal., 172 (2004), 247-266.
doi: 10.1007/s00205-003-0304-3. |
show all references
References:
[1] |
R. Aris, Prolegomena to the rational analysis of systems of chemical reactions, Archiv. Rat. Mech. Anal., 19 (1965), 81-99. |
[2] |
R. J. Bearman and J. G. Kirkwood, The statistical mechanics of transport processes. XI. Equations of transport in multicomponent systems, J. Chem. Phys., 28 (1958), 136-145. |
[3] |
H. Van Beijeren and M. H. Ernst, The modified enskog equations, Phys. A, 68 (1973), 437-456. |
[4] |
H. Van Beijeren and M. H. Ernst, The modified enskog equations for mixtures, Phys. A, 70 (1973), 225-242. |
[5] |
R. Bendahklia, V. Giovangigli and D. Rosner, Soret effects in laminar counterflow spray diffusion flames, Comb. Theory Mod., 6 (2002), 1-17. |
[6] |
G. Billet, V. Giovangigli and G. de Gassowski, Impact of volume viscosity on a shock-hydrogen bubble interaction, Comb. Theory Mod., 12 (2008), 221-248.
doi: 10.1080/13647830701545875. |
[7] |
D. Bresch and B. Desjardins, On the existence of global weak solutions to the Navier-Stokes equations for viscous compressible and heat conducting fluids, J. Math. Pure Appl., 87 (2007), 57-90.
doi: 10.1016/j.matpur.2006.11.001. |
[8] |
S. Chapman and T. G. Cowling, "The Mathematical Theory of Non-Uniform Gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases," Third edition, prepared in co-operation with D. Burnett, Cambridge University Press, London, 1970. |
[9] |
G. Q. Chen, C. D. Levermore and T.-P. Liu, Hyperbolic conservation laws with stiff relaxation terms and entropy, Comm. Pure Appl. Math., 47 (1994), 787-830.
doi: 10.1002/cpa.3160470602. |
[10] |
J.-P. Croisille and P. Delorme, Kinetic symmetrizations and pressure laws for the Euler equations, Physica D, 57 (1992), 395-416.
doi: 10.1016/0167-2789(92)90010-K. |
[11] |
C. Dafermos, "Hyperbolic Conservation Laws in Continuum Physics," Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 325, Springer-Verlag, Berlin, 2000.
doi: 10.1007/3-540-29089-3_14. |
[12] |
P. Degond, S. Genieys and A. Jüengel, A system of parabolic equations in nonequilibrium thermodynamics including thermal and electric effects, J. Math. Pure Appl., 160 (1997), 991-1015. |
[13] |
S. R. de Groot and P. Mazur, "Non-Equilibrium Thermodynamics," Dover publications, Inc., New York, 1984. |
[14] |
A. Ern and V. Giovangigli, Thermal diffusion effects in hydrogen-air and methane-air flames, Comb. Theory Mod., 2-4 (1998), 349-372. |
[15] |
A. Ern and V. Giovangigli, "Multicomponent Transport Algorithms," Lecture Notes in Physics, New Series m: Monographs, 24, Springer-Verlag, Berlin, 1994. |
[16] |
A. Ern and V. Giovangigli, Thermal conduction and thermal diffusion in dilute polyatomic gas mixtures, Physica A, 214 (1995), 526-546. |
[17] |
A. Ern and V. Giovangigli, Structure of transport linear systems in dilute isotropic gas mixtures, Phys. Rev. E (3), 53 (1996), 485-492.
doi: 10.1103/PhysRevE.53.485. |
[18] |
A. Ern and V. Giovangigli, Optimized transport algorithms for flame codes, Comb. Sci. Tech., 118 (1996), 387-395. |
[19] |
A. Ern and V. Giovangigli, Projected iterative algorithms with application to multicomponent transport, Linear Algebra Appl., 250 (1997), 289-315.
doi: 10.1016/0024-3795(95)00502-1. |
[20] |
A. Ern and V. Giovangigli, The Kinetic equilibrium regime, Physica A, 260 (1998), 49-72. |
[21] |
L. C. Evans, A survey of entropy methods for partial differential equations, Bulletin of the AMS (N.S.), 41 (2004), 409-438.
doi: 10.1090/S0273-0979-04-01032-8. |
[22] |
E. Feireisl, "Dynamics of Viscous Compressible Fluids," Oxford Lecture Series in Mathematics and its Applications, 26, Oxford University Press, Oxford, 2004. |
[23] |
J. H. Ferziger and H. G. Kaper, "Mathematical Theory of Transport Processes in Gases," North-Holland Publishing Company, Amsterdam, 1972. |
[24] |
K. O. Friedrichs and P. D. Lax, Systems of conservation laws with a convex extension, Proc. Nat. Acad. Sci. USA, 68 (1971), 1686-1688. |
[25] |
W. H. Furry, On the elementary explanation of diffusion phenomena in gases, Am. J. Phys., 16 (1948), 63-78. |
[26] |
V. Giovangigli, Convergent iterative methods for multicomponent diffusion, Impact Comput. Sci. Eng., 3 (1991), 244-276.
doi: 10.1016/0899-8248(91)90010-R. |
[27] |
V. Giovangigli, "Multicomponent Flow Modeling," Modeling and Simulation in Science, Engineering and Technology, Birkhäuser Boston, Inc., Boston, MA, 1999.
doi: 10.1007/978-1-4612-1580-6. |
[28] |
V. Giovangigli, Persistence of Boltzmann entropy in fluid models, Disc. Cont. Dyn. Syst., 24 (2009), 95-114.
doi: 10.3934/dcds.2009.24.95. |
[29] |
V. Giovangigli, Higher order entropies, Arch. Rat. Mech. Anal., 187 (2008), 221-285.
doi: 10.1007/s00205-007-0065-5. |
[30] |
V. Giovangigli, Higher order entropies for compressible fluid models, Math. Mod. Meth. Appl. Sci., 19 (2009), 67-125.
doi: 10.1142/S021820250900336X. |
[31] |
V. Giovangigli, Multicomponent transport algorithms for partially ionized mixtures, J. Comp. Phys., 229 (2010), 4117-4142.
doi: 10.1016/j.jcp.2010.02.001. |
[32] |
V. Giovangigli and M. Massot, Asymptotic stability of equilibrium states for multicomponent reactive flows, Math. Mod. Meth. App. Sci., 8 (1998), 251-297.
doi: 10.1142/S0218202598000123. |
[33] |
V. Giovangigli and M. Massot, Entropic structure of multicomponent reactive flows with partial equilibrium reduced chemistry, Math. Meth. Appl. Sci., 27 (2004), 739-768.
doi: 10.1002/mma.429. |
[34] |
V. Giovangigli and L. Matuszewski, Supercritical fluid thermodynamics from equations of state, Phys. D, 241 (2012), 649-670.
doi: 10.1016/j.physd.2011.12.002. |
[35] |
V. Giovangigli and L. Matuszewski, Mathematical modeling of supercritical multicomponent reactive fluids, to appear, M3AS, (2012). |
[36] |
V. Giovangigli, L. Matuszewski and F. Dupoirieux, Detailed modeling of planar transcritical $H_2$-$O_2$-$N_2$ flames, Combustion Theory and Modelling, 15 (2011), 141-182. |
[37] |
V. Giovangigli and B. Tran, Mathematical analysis of a Saint-Venant model with variable temperature, Math. Mod. Meth. Appl. Sci., 20 (2010), 1251-1297.
doi: 10.1142/S0218202510004593. |
[38] |
A. Glitzky, K. Gröger and R. Hünlich, Free energy and dissipation rate for reaction diffusion processes of electrically charged species, Appl. Anal., 60 (1996), 201-217.
doi: 10.1080/00036819608840428. |
[39] |
S. Godunov, An interesting class of quasilinear systems, Sov. Math. Dokl., 2 (1961), 947-949. |
[40] |
E. A. Guggenheim, "Thermodynamics," North Holland, Amsterdam, 1962. |
[41] |
J. O. Hirschfelder, C. F. Curtiss and R. B. Bird, "Molecular Theory of Gases and Liquids," Wiley, New York, 1954. |
[42] |
T. J. R. Hughes, L. P. Franca and M. Mallet, A new finite element formulation for computational fluid dynamics. I. Symmetric forms of the compressible Euler and Navier-Stokes equations and the second law of thermodynamics, Comp. Meth. Appl. Mech. Eng., 54 (1986), 223-234.
doi: 10.1016/0045-7825(86)90127-1. |
[43] |
J. H. Irving and J. G. Kirkwood, The statistical mechanical theory of transport processes. IV. The equations of hydrodynamics, J. Chem. Phys., 18 (1950), 817-829. |
[44] |
A. Jüengel and I. Stelzer, Existence analysis of Maxwell-Stefan systems for multicomponent mixtures, arXiv:1211.2394, (2012). |
[45] |
S. Kawashima, "Systems of a Hyperbolic-Parabolic Composite Type, with Applications to the Equations of Magnetohydrodynamics," Doctoral Thesis, Kyoto University, 1984. |
[46] |
S. Kawashima, Large-time behavior of solutions to hyperbolic-parabolic systems of conservations laws and applications, Proc. Roy. Soc. Edinburgh Sect. A, 106 (1987), 169-194.
doi: 10.1017/S0308210500018308. |
[47] |
S. Kawashima and Y. Shizuta, On the normal form of the symmetric hyperbolic-parabolic systems associated with the conservation laws, Tohoku Math. J. (2), 40 (1988), 449-464.
doi: 10.2748/tmj/1178227986. |
[48] |
S. Kawashima and W.-A. Yong, Dissipative structure and entropy for hyperbolic systems of conservation laws, Arch. Rat. Mech. Anal., 174 (2004), 345-364.
doi: 10.1007/s00205-004-0330-9. |
[49] |
J. Keizer, "Statistical Thermodynamics of Nonequilibrium Processes," Springer-Verlag, New York, 1987. |
[50] |
F. J. Krambeck, The mathematical structure of chemical kinetics in homogeneous single-phase systems, Arch. Rational Mech. Anal., 38 (1970), 317-347.
doi: 10.1007/BF00251527. |
[51] |
V. I. Kurochkin, S. F. Makarenko and G. A. Tirskii, Transport coefficients and the Onsager relations in the kinetic theroy of dense gas mixtures, J. Appl. Mech. Tech. Phys., 25 (1984), 218-225. |
[52] |
P.-L. Lions, B. Perthame and E. Tadmor, Kinetic formulation of the isentropic gas dynamics and $p$-systems, Comm. Math. Phys., 163 (1994), 415-431. |
[53] |
M. R. Marcelin, "Sur la Mécanique des Phénomènes Irréversibles," Comptes Rendus de l'Académie des Sciences de Paris, Séance du 5 décembre 1910, (1910), 1052-1055. |
[54] |
J. Meixner, Zur Thermodynamik der irreversiblen Prozesse in Gasen mit chemisch reagierenden, dissoziierenden und anregbaren Komponenten, Ann. der Phys., 43 (1943), 244-270. |
[55] |
H. Mori, Statistical-mechanical theory of transport in fluids, Phys. Rev., 112 (1958), 1829-1842. |
[56] |
I. Prigogine, "Etude Thermodynamique des Phénomènes Irréversibles," Dunod, Paris, 1947. |
[57] |
J. Pousin, "Modélisation et Analyse Numérique de Couches Limites Réactives d'Air," Doctorat es Sciences, Ecole Polytechnique Fédérale de Lausanne, 1112, 1993. |
[58] |
T. Ruggeri, Thermodynamics and Symmetric Hyperbolic Systems. Nonlinear hyperbolic equations in applied sciences,, Rend. Sem. Mat. Univ. Politec. Torino, 1988 (): 167.
|
[59] |
N. Z. Shapiro and L. S. Shapley, Mass action law and the Gibbs free energy function, SIAM J. Appl. Math., 13 (1965), 353-375. |
[60] |
D. Serre, Systèmes de Lois de Conservation. I et II, Diderot Editeur, Paris, 1996. |
[61] |
D. Serre, The structure of dissipative viscous system of conservation laws, Physica D, 239 (2010), 1381-1386.
doi: 10.1016/j.physd.2009.03.014. |
[62] |
Y. Shizuta and S. Kawashima, Systems of Equations of hyperbolic-parabolic type with applications to the discrete Boltzmann equation, Hokkaido Math. J., 14 (1985), 249-275. |
[63] |
R. Taylor and R. Krishna, "Multicomponent Mass Transfer," John Wiley, New York, 1993. |
[64] |
T. Umeda, S. Kawashima and Y. Shizuta, On the Decay of solutions to the linearized equations of electromagnetofluid dynamics, Japan J. Appl. Math., 1 (1984), 435-457.
doi: 10.1007/BF03167068. |
[65] |
J. Van de Ree, On the definition of the diffusion coefficients in reacting gases, Physica, 36 (1967), 118-126. |
[66] |
A. I. Vol'pert and S. I. Hudjaev, On the Cauchy problem for composite systems of nonlinear differential equations, Mat. Sb. (N.S.), 87(129) (1972), 504-528. |
[67] |
L. G. Vulkov, On the conservation laws of the Compressible euler equations, Applicable Analysis, 64 (1997), 255-271.
doi: 10.1080/00036819708840534. |
[68] |
L. Waldmann, Transporterscheinungen in Gasen von mittlerem Druck, in "1958 Handbuch der Physik," Bd. 12, Thermodynamik der Gase, Springer-Verlag, Berlin-Göttingen-Heidelberg, (1958), 295-514. |
[69] |
J. Wei, An axiomatic treatment of chemical reaction systems, J. Chem. Phys., 36 (1962), 1578-1584. |
[70] | |
[71] |
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