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A mathematical and numerical analysis of the Maxwell-Stefan diffusion equations
1. | UPMC Univ Paris 06, UMR 7598 LJLL, Paris, F-75005 |
2. | INRIA Paris-Rocquencourt, REO Project team, BP 105, 78153 Le Chesnay, France, France |
References:
[1] |
M. Bebendorf, A note on the Poincaré inequality for convex domains,, Z. Anal. Anwendungen, 22 (2003), 751.
doi: 10.4171/ZAA/1170. |
[2] |
M. Bendahmane, T. Lepoutre, A. Marrocco and B. Perthame, Conservative cross diffusions and pattern formation through relaxation,, J. Math. Pures Appl. (9), 92 (2009), 651.
doi: 10.1016/j.matpur.2009.05.003. |
[3] |
L. Boudin, D. Götz and B. Grec, Diffusion models of multicomponent mixtures in the lung,, in, 30 (2010), 90.
|
[4] |
L. Boudin, B. Grec and F. Salvarani, The Maxwell-Stefan diffusion limit for a kinetic model of mixtures,, HAL preprint, (2011). Google Scholar |
[5] |
H. K. Chang, Multicomponent diffusion in the lung,, Fed. Proc., 39 (1980), 2759. Google Scholar |
[6] |
L. Chen and A. Jüngel, Analysis of a multidimensional parabolic population model with strong cross-diffusion,, SIAM J. Math. Anal., 36 (2004), 301.
|
[7] |
J. Crank, "The Mathematics of Diffusion,'', 2nd edition, (1975).
|
[8] |
H. Darcy, "Les Fontaines Publiques de la Ville de Dijon,'', V. Dalmont, (1856). Google Scholar |
[9] |
J. B. Duncan and H. L. Toor, An experimental study of three component gas diffusion,, AIChE Journal, 8 (1962), 38. Google Scholar |
[10] |
A. Ern and V. Giovangigli, "Multicomponent Transport Algorithms,'', Lecture Notes in Physics, 24 (1994).
|
[11] |
A. Ern and V. Giovangigli, Projected iterative algorithms with application to multicomponent transport,, Linear Algebra Appl., 250 (1997), 289.
doi: 10.1016/0024-3795(95)00502-1. |
[12] |
L. C. Evans, "Partial Differential Equations,'', 2nd edition, 19 (2010).
|
[13] |
A. Fick, On liquid diffusion,, Phil. Mag., 10 (1855), 30. Google Scholar |
[14] |
A. Fick, Über Diffusion,, Poggendorff's Annalen der Physik und Chemie, 94 (1855), 59.
doi: 10.1002/andp.18551700105. |
[15] |
V. Giovangigli, Convergent iterative methods for multicomponent diffusion,, Impact Comput. Sci. Engrg., 3 (1991), 244.
doi: 10.1016/0899-8248(91)90010-R. |
[16] |
V. Giovangigli, "Multicomponent Flow Modeling,'', Modeling and Simulation in Science, (1999).
doi: 10.1007/978-1-4612-1580-6. |
[17] |
R. Krishna and J. A. Wesselingh, The Maxwell-Stefan approach to mass transfer,, Chem. Eng. Sci., 52 (1997), 861.
doi: 10.1016/S0009-2509(96)00458-7. |
[18] |
O. A. Ladyženskaja, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type,'', Translations of Mathematical Monographs, (1967).
|
[19] |
Y. Lou and W.-M. Ni, Diffusion, self-diffusion and cross-diffusion,, J. Differential Equations, 131 (1996), 79.
doi: 10.1006/jdeq.1996.0157. |
[20] |
J. C. Maxwell, On the dynamical theory of gases,, Phil. Trans. R. Soc., 157 (1866), 49.
doi: 10.1098/rstl.1867.0004. |
[21] |
L. E. Payne and H. F. Weinberger, An optimal Poincaré inequality for convex domains,, Arch. Rational Mech. Anal., 5 (1960), 286.
doi: 10.1007/BF00252910. |
[22] |
J. Stefan, Über das Gleichgewicht und die Bewegung insbesondere die Diffusion von Gasgemengen,, Akad. Wiss. Wien, 63 (1871), 63. Google Scholar |
[23] |
M. Thiriet, D. Douguet, J.-C. Bonnet, C. Canonne and C. Hatzfeld, The effect on gas mixing of a He-$\mboxO_2$ mixture in chronic obstructive lung diseases,, Bull. Eur. Physiopathol. Respir., 15 (1979), 1053. Google Scholar |
[24] |
J. L. Vázquez, "The Porous Medium Equation. Mathematical Theory,'', Oxford Mathematical Monographs, (2007).
|
[25] |
F. A. Williams, "Combustion Theory,'', 2nd edition, (1985). Google Scholar |
show all references
References:
[1] |
M. Bebendorf, A note on the Poincaré inequality for convex domains,, Z. Anal. Anwendungen, 22 (2003), 751.
doi: 10.4171/ZAA/1170. |
[2] |
M. Bendahmane, T. Lepoutre, A. Marrocco and B. Perthame, Conservative cross diffusions and pattern formation through relaxation,, J. Math. Pures Appl. (9), 92 (2009), 651.
doi: 10.1016/j.matpur.2009.05.003. |
[3] |
L. Boudin, D. Götz and B. Grec, Diffusion models of multicomponent mixtures in the lung,, in, 30 (2010), 90.
|
[4] |
L. Boudin, B. Grec and F. Salvarani, The Maxwell-Stefan diffusion limit for a kinetic model of mixtures,, HAL preprint, (2011). Google Scholar |
[5] |
H. K. Chang, Multicomponent diffusion in the lung,, Fed. Proc., 39 (1980), 2759. Google Scholar |
[6] |
L. Chen and A. Jüngel, Analysis of a multidimensional parabolic population model with strong cross-diffusion,, SIAM J. Math. Anal., 36 (2004), 301.
|
[7] |
J. Crank, "The Mathematics of Diffusion,'', 2nd edition, (1975).
|
[8] |
H. Darcy, "Les Fontaines Publiques de la Ville de Dijon,'', V. Dalmont, (1856). Google Scholar |
[9] |
J. B. Duncan and H. L. Toor, An experimental study of three component gas diffusion,, AIChE Journal, 8 (1962), 38. Google Scholar |
[10] |
A. Ern and V. Giovangigli, "Multicomponent Transport Algorithms,'', Lecture Notes in Physics, 24 (1994).
|
[11] |
A. Ern and V. Giovangigli, Projected iterative algorithms with application to multicomponent transport,, Linear Algebra Appl., 250 (1997), 289.
doi: 10.1016/0024-3795(95)00502-1. |
[12] |
L. C. Evans, "Partial Differential Equations,'', 2nd edition, 19 (2010).
|
[13] |
A. Fick, On liquid diffusion,, Phil. Mag., 10 (1855), 30. Google Scholar |
[14] |
A. Fick, Über Diffusion,, Poggendorff's Annalen der Physik und Chemie, 94 (1855), 59.
doi: 10.1002/andp.18551700105. |
[15] |
V. Giovangigli, Convergent iterative methods for multicomponent diffusion,, Impact Comput. Sci. Engrg., 3 (1991), 244.
doi: 10.1016/0899-8248(91)90010-R. |
[16] |
V. Giovangigli, "Multicomponent Flow Modeling,'', Modeling and Simulation in Science, (1999).
doi: 10.1007/978-1-4612-1580-6. |
[17] |
R. Krishna and J. A. Wesselingh, The Maxwell-Stefan approach to mass transfer,, Chem. Eng. Sci., 52 (1997), 861.
doi: 10.1016/S0009-2509(96)00458-7. |
[18] |
O. A. Ladyženskaja, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type,'', Translations of Mathematical Monographs, (1967).
|
[19] |
Y. Lou and W.-M. Ni, Diffusion, self-diffusion and cross-diffusion,, J. Differential Equations, 131 (1996), 79.
doi: 10.1006/jdeq.1996.0157. |
[20] |
J. C. Maxwell, On the dynamical theory of gases,, Phil. Trans. R. Soc., 157 (1866), 49.
doi: 10.1098/rstl.1867.0004. |
[21] |
L. E. Payne and H. F. Weinberger, An optimal Poincaré inequality for convex domains,, Arch. Rational Mech. Anal., 5 (1960), 286.
doi: 10.1007/BF00252910. |
[22] |
J. Stefan, Über das Gleichgewicht und die Bewegung insbesondere die Diffusion von Gasgemengen,, Akad. Wiss. Wien, 63 (1871), 63. Google Scholar |
[23] |
M. Thiriet, D. Douguet, J.-C. Bonnet, C. Canonne and C. Hatzfeld, The effect on gas mixing of a He-$\mboxO_2$ mixture in chronic obstructive lung diseases,, Bull. Eur. Physiopathol. Respir., 15 (1979), 1053. Google Scholar |
[24] |
J. L. Vázquez, "The Porous Medium Equation. Mathematical Theory,'', Oxford Mathematical Monographs, (2007).
|
[25] |
F. A. Williams, "Combustion Theory,'', 2nd edition, (1985). Google Scholar |
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