-
Previous Article
Asymptotic behavior for a stochastic wave equation with dynamical boundary conditions
- DCDS-B Home
- This Issue
-
Next Article
Time-averaging and permanence in nonautonomous competitive systems of PDEs via Vance-Coddington estimates
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), 751-756.
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. |
show all references
References:
[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. |
[1] |
B. Anwasia, M. Bisi, F. Salvarani, A. J. Soares. On the Maxwell-Stefan diffusion limit for a reactive mixture of polyatomic gases in non-isothermal setting. Kinetic and Related Models, 2020, 13 (1) : 63-95. doi: 10.3934/krm.2020003 |
[2] |
Pierre-Etienne Druet. A theory of generalised solutions for ideal gas mixtures with Maxwell-Stefan diffusion. Discrete and Continuous Dynamical Systems - S, 2021, 14 (11) : 4035-4067. doi: 10.3934/dcdss.2020458 |
[3] |
Andrea Bondesan, Marc Briant. Perturbative Cauchy theory for a flux-incompressible Maxwell-Stefan system. Discrete and Continuous Dynamical Systems, 2022, 42 (6) : 2747-2773. doi: 10.3934/dcds.2021210 |
[4] |
Laurent Boudin, Bérénice Grec, Milana Pavić, Francesco Salvarani. Diffusion asymptotics of a kinetic model for gaseous mixtures. Kinetic and Related Models, 2013, 6 (1) : 137-157. doi: 10.3934/krm.2013.6.137 |
[5] |
W. Wei, H. M. Yin. Global solvability for a singular nonlinear Maxwell's equations. Communications on Pure and Applied Analysis, 2005, 4 (2) : 431-444. doi: 10.3934/cpaa.2005.4.431 |
[6] |
Björn Birnir, Niklas Wellander. Homogenized Maxwell's equations; A model for ceramic varistors. Discrete and Continuous Dynamical Systems - B, 2006, 6 (2) : 257-272. doi: 10.3934/dcdsb.2006.6.257 |
[7] |
Annalena Albicker, Roland Griesmaier. Monotonicity in inverse scattering for Maxwell's equations. Inverse Problems and Imaging, , () : -. doi: 10.3934/ipi.2022032 |
[8] |
L. Chupin. Existence result for a mixture of non Newtonian flows with stress diffusion using the Cahn-Hilliard formulation. Discrete and Continuous Dynamical Systems - B, 2003, 3 (1) : 45-68. doi: 10.3934/dcdsb.2003.3.45 |
[9] |
Gang Bao, Bin Hu, Peijun Li, Jue Wang. Analysis of time-domain Maxwell's equations in biperiodic structures. Discrete and Continuous Dynamical Systems - B, 2020, 25 (1) : 259-286. doi: 10.3934/dcdsb.2019181 |
[10] |
M. Eller. On boundary regularity of solutions to Maxwell's equations with a homogeneous conservative boundary condition. Discrete and Continuous Dynamical Systems - S, 2009, 2 (3) : 473-481. doi: 10.3934/dcdss.2009.2.473 |
[11] |
Oleg Yu. Imanuvilov, Masahiro Yamamoto. Calderón problem for Maxwell's equations in cylindrical domain. Inverse Problems and Imaging, 2014, 8 (4) : 1117-1137. doi: 10.3934/ipi.2014.8.1117 |
[12] |
Jiangxing Wang. Convergence analysis of an accurate and efficient method for nonlinear Maxwell's equations. Discrete and Continuous Dynamical Systems - B, 2021, 26 (5) : 2429-2440. doi: 10.3934/dcdsb.2020185 |
[13] |
Hao Wang, Wei Yang, Yunqing Huang. An adaptive edge finite element method for the Maxwell's equations in metamaterials. Electronic Research Archive, 2020, 28 (2) : 961-976. doi: 10.3934/era.2020051 |
[14] |
B. L. G. Jonsson. Wave splitting of Maxwell's equations with anisotropic heterogeneous constitutive relations. Inverse Problems and Imaging, 2009, 3 (3) : 405-452. doi: 10.3934/ipi.2009.3.405 |
[15] |
Cleverson R. da Luz, Gustavo Alberto Perla Menzala. Uniform stabilization of anisotropic Maxwell's equations with boundary dissipation. Discrete and Continuous Dynamical Systems - S, 2009, 2 (3) : 547-558. doi: 10.3934/dcdss.2009.2.547 |
[16] |
Andreas Kirsch. An integral equation approach and the interior transmission problem for Maxwell's equations. Inverse Problems and Imaging, 2007, 1 (1) : 159-179. doi: 10.3934/ipi.2007.1.159 |
[17] |
Wafa Hamrouni, Ali Abdennadher. Random walk's models for fractional diffusion equation. Discrete and Continuous Dynamical Systems - B, 2016, 21 (8) : 2509-2530. doi: 10.3934/dcdsb.2016058 |
[18] |
Massimiliano Berti. Some remarks on a variational approach to Arnold's diffusion. Discrete and Continuous Dynamical Systems, 1996, 2 (3) : 307-314. doi: 10.3934/dcds.1996.2.307 |
[19] |
Dirk Pauly. On Maxwell's and Poincaré's constants. Discrete and Continuous Dynamical Systems - S, 2015, 8 (3) : 607-618. doi: 10.3934/dcdss.2015.8.607 |
[20] |
Kim Dang Phung. Energy decay for Maxwell's equations with Ohm's law in partially cubic domains. Communications on Pure and Applied Analysis, 2013, 12 (5) : 2229-2266. doi: 10.3934/cpaa.2013.12.2229 |
2021 Impact Factor: 1.497
Tools
Metrics
Other articles
by authors
[Back to Top]