Citation: |
[1] |
M. Bebendorf, A note on the Poincaré inequality for convex domains, Z. Anal. Anwendungen, 22 (2003), 751-756.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), 651-667.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 "CEMRACS 2009: Mathematical Modelling in Medicine," ESAIM Proc., 30, EDP Sci., Les Ulis, (2010), 90-103. |
[4] |
L. Boudin, B. Grec and F. Salvarani, The Maxwell-Stefan diffusion limit for a kinetic model of mixtures, HAL preprint, submitted, 2011. Available from: http://hal.archives-ouvertes.fr/hal-00554744. |
[5] |
H. K. Chang, Multicomponent diffusion in the lung, Fed. Proc., 39 (1980), 2759-2764. |
[6] |
L. Chen and A. Jüngel, Analysis of a multidimensional parabolic population model with strong cross-diffusion, SIAM J. Math. Anal., 36 (2004), 301-322. |
[7] |
J. Crank, "The Mathematics of Diffusion,'' 2nd edition, Clarendon Press, Oxford, 1975. |
[8] |
H. Darcy, "Les Fontaines Publiques de la Ville de Dijon,'' V. Dalmont, Paris, 1856. |
[9] |
J. B. Duncan and H. L. Toor, An experimental study of three component gas diffusion, AIChE Journal, 8 (1962), 38-41. |
[10] |
A. Ern and V. Giovangigli, "Multicomponent Transport Algorithms,'' Lecture Notes in Physics, New Series m: Monographs, 24, Springer-Verlag, Berlin, 1994. |
[11] |
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. |
[12] |
L. C. Evans, "Partial Differential Equations,'' 2nd edition, Graduate Studies in Mathematics, 19, American Mathematical Society, Providence, RI, 2010. |
[13] | |
[14] |
A. Fick, Über Diffusion, Poggendorff's Annalen der Physik und Chemie, 94 (1855), 59-86.doi: 10.1002/andp.18551700105. |
[15] |
V. Giovangigli, Convergent iterative methods for multicomponent diffusion, Impact Comput. Sci. Engrg., 3 (1991), 244-276.doi: 10.1016/0899-8248(91)90010-R. |
[16] |
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. |
[17] |
R. Krishna and J. A. Wesselingh, The Maxwell-Stefan approach to mass transfer, Chem. Eng. Sci., 52 (1997), 861-911.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, Vol. 23, American Mathematical Society, Providence, R.I., 1967. |
[19] |
Y. Lou and W.-M. Ni, Diffusion, self-diffusion and cross-diffusion, J. Differential Equations, 131 (1996), 79-131.doi: 10.1006/jdeq.1996.0157. |
[20] |
J. C. Maxwell, On the dynamical theory of gases, Phil. Trans. R. Soc., 157 (1866), 49-88.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), 286-292.doi: 10.1007/BF00252910. |
[22] |
J. Stefan, Über das Gleichgewicht und die Bewegung insbesondere die Diffusion von Gasgemengen, Akad. Wiss. Wien, 63 (1871), 63-124. |
[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), 1053-1068. |
[24] |
J. L. Vázquez, "The Porous Medium Equation. Mathematical Theory,'' Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, Oxford, 2007. |
[25] |
F. A. Williams, "Combustion Theory,'' 2nd edition, Benjamin Cummings, 1985. |