Reactive transport through an array of cells with semi-permeable membranes

U. Hornung; W. Jäger; A. Mikelić

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1994)

  • Volume: 28, Issue: 1, page 59-94
  • ISSN: 0764-583X

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Hornung, U., Jäger, W., and Mikelić, A.. "Reactive transport through an array of cells with semi-permeable membranes." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 28.1 (1994): 59-94. <http://eudml.org/doc/193731>.

@article{Hornung1994,
author = {Hornung, U., Jäger, W., Mikelić, A.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {nonlinear transmission conditions; diffusion; convection; viscous incompressible fluid; limit process; two-scale convergence},
language = {eng},
number = {1},
pages = {59-94},
publisher = {Dunod},
title = {Reactive transport through an array of cells with semi-permeable membranes},
url = {http://eudml.org/doc/193731},
volume = {28},
year = {1994},
}

TY - JOUR
AU - Hornung, U.
AU - Jäger, W.
AU - Mikelić, A.
TI - Reactive transport through an array of cells with semi-permeable membranes
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1994
PB - Dunod
VL - 28
IS - 1
SP - 59
EP - 94
LA - eng
KW - nonlinear transmission conditions; diffusion; convection; viscous incompressible fluid; limit process; two-scale convergence
UR - http://eudml.org/doc/193731
ER -

References

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  1. [1] I. AGANOVIĆ, A. MIKELIĆ, 1992, Homogenization of nonstationary flow of a two-constituent mixture through a porous medium, Asymptotic Analysis, 6, 173-189. Zbl0763.76077MR1193110
  2. [2] G. ALLAIRE, 1989, Homogenization of the Stokes flow in a connected porous medium, Asympt. Anal, 2, 203-222. Zbl0682.76077MR1020348
  3. [3] G. ALLAIRE, 1991, Homogénéisation et convergence à deux échelles. Application à un problème de convection diffusion, C. R. Acad. Sci. Paris, 312, Ser. I, 581-586. Zbl0724.46033MR1101037
  4. [4] T. ARBOGAST, J. DOUGLAS, U. HORNUNG, 1990, Derivation of the double porosity model of single phase fiow via homogenization theory, SIAM J. Math. Anal., 21, 823-836. Zbl0698.76106MR1052874
  5. [5] T. ARBOGAST, J. DOUGLAS, U. HORNUNG, 1991, Modeling of naturally fractured reservoirs by formai homogenization techniques, Dautray R. (Ed.) Froutiers in Pure and Applied Mathematics, Elsevier, Amsterdam, 1-19. Zbl0727.76110MR1110588
  6. [6] N. BAKHVALOV, G. PANASENKO, 1989, Homogenization : Averaging Processes in Periodic Media, Kluwer, Dordrecht. Zbl0692.73012MR1112788
  7. [7] A. BENSOUSSAN, J. L. LIONS, G. PAPANICOLAOU, 1978, Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam. Zbl0404.35001MR503330
  8. [8] A. P. BOURGEAT, 1985, Nonlinear homogenization of two-phase flow equations J. H. Lightbourne, S. M. Rankin (Eds), Physical Mathematics and Nonlinear Partial Differential Equations, 207-212. Zbl0617.76117MR826836
  9. [9] A. P. BOURGEAT, 1986, Homogenization of two-phase flow equations, Proceedings Symposia Pure Mathem., 45, 157-163. Zbl0641.76094MR843558
  10. [10] H. BRÉZIS, 1972, Problèmes unilatéraux, J. Math. pures et appl., 51, 1-168. Zbl0237.35001MR428137
  11. [11] E. CANON, W. JÄGER, Homogenization for nonlinear adsorption-diffusion processes in porous media, to appear. 
  12. [12] D. CIORANESCU, J. SAINT-JEAN-PAULIN, 1979, Homogenization in open sets with holes, J. Math. Anal. Appl., 71, 590-607. Zbl0427.35073MR548785
  13. [13] I. EKELAND, R. TEMAM, 1976, Convex Analysis and Variational Problems, North-Holland, Amsterdam. Zbl0322.90046MR463994
  14. [14] A. FRIEDMAN, P. KNABNER, A Transport Model with Micro-and Macro-Structure, J. Differ. Equ., to appear. Zbl0749.76073
  15. [15] K. GROGER, 1971, Zum Rand-Anfangswertproblem der Adsorption und Diffusion bei Festbettprozessen, Mathem. Nachr., 49, 251-259. Zbl0307.35078MR312832
  16. [16] U. HORNUNG, 1991, Homogenization of Miscible Displacement in Unsaturated Aggregated Soils, G. Dal Maso, G. F. Dell'Antonio (Eds.) Composite Media and Homogenization Theory, Progress in Nonlinear Differential Equations and Their Applications, Birkhäuser, Boston, 143-153. Zbl0726.73061MR1145749
  17. [17] U. HORNUNG, 1991, Miscible displacement in porous media influenced by mobile and immobile water, Rocky Mountain J. Math., 21, 645-669 corr. 1153-1158. Zbl0751.76062MR1121532
  18. [18] U. HORNUNG, 1992, Applications of the homogenization method to flow and transport in porous media Xiao Shutie (Ed.) Summer School on Flow and Transport in Porous Media, World Scientific Publisher, Singapore, 167-222. Zbl0790.76092
  19. [19] U. HORNUNG, W. JÄGER, 1987, A model for chemical reactions in porous media J. Warnatz, W. Jäger (Eds.) Complex Chemical Reaction Systems. Mathematical Modeling and Simulation, Chemical Physics, 47, 318-334. MR924854
  20. [20] U. HORNUNG, W. JÄGER, 1991, Diffusion, convection, adsorption, and reaction of chemicals in porous media, J. Differ. Equat., 92, 199-225. Zbl0731.76080MR1120903
  21. [21] U. HORNUNG, R. SHOWALTER, 1990, Diffusion models for fractured media, J. Math. Anal. Applics, 147, 69-80. Zbl0703.76080MR1044687
  22. [22] J. L. LIONS, 1969, Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Dunod/Gauthier-Villars, Paris. Zbl0189.40603MR259693
  23. [23] R. LIPTON, A. AVELLANEDA, 1990, A Darcy law for slow viscous flow past a stationary array of bubbles, Proc. Royal Soc. Edinburgh, 114A, 71-79. Zbl0850.76778
  24. [24] A. MIKELIĆ, 1989, A convergence theorem for homogenization of two-phase miscible flow through fractured reservoirs with uniform fracture distributions, Applicable Analysis, 33, 203-214. Zbl0653.76067MR1030108
  25. [25] A. MIKELIĆ, 1991, Homogenization of nonstationary Navier-Stokes equations in a domain with grained boundary, Ann, Mat. Pura e Appl., 158, 167-179. Zbl0758.35007MR1131849
  26. [26] A. MIKELIĆ, I. AGANOVIĆ, 1987, Homogenization in a porous medium under a nonhomogeneous boundary condition, Boll. Un. Mat. Ital. (A) 1, 171-180. Zbl0629.76102MR898276
  27. [27] A. MIKELIĆ, I. AGANOVIĆ, 1988, Homogenization of stationary flow of miscible fluids in a domain with a grained boundary, SIAM J. Math. Anal., 19, 287-294. Zbl0645.76099MR930027
  28. [28] F. MURAT, 1978, Compacité par compensation, Ann. Scuola Norm. Sup. Pisa, Ser. 4, 5, 489-507. Zbl0399.46022MR506997
  29. [29] G. NGUETSENG, 1989, A general convergence result for a functional related to the theory of homogenization, SIAM J. Math. Anal., 20, 608-623. Zbl0688.35007MR990867
  30. [30] O. A. OLEINIK, S. M. KOZLOV, V. V. ZHIKOV, 1991, Homogenization Differential Operators, North-Holland, Amsterdam. 
  31. [31] E. SANCHEZ-PALENCIA, 1980, Non-Homogeneous Media and Vibration Theory, Springer Lecture Notes in Physics, 129. Zbl0432.70002MR578345
  32. [32] K. SATTEL-SCHWIND, 1988, Untersuchung über Diffusionsvorgänge bei der Gelpermeations-Chromatographie von Poly-p-Methylstyrol, Dissertation, Fachbereich Chemie, Universität Heidelberg. 
  33. [33] K. SIEBEL, 1988, Diffusion in dispersen Medien. Homogenisierung, Diplomarbeit Fachbereich Mathematik, Universitat Heidelberg. 
  34. [34] J. SIMON, 1987, Compact sets in the space Lp(0, T ; B), Ann. Mat. Pura e Appl., 145, 65-96. Zbl0629.46031MR916688
  35. [35] L. TARTAR, 1980, Incompressible fluid flow in a porous medium - convergence of the homogenization process, E. Sanchez-Palencia (Ed.) « Non-homogeneous media and vibration theory » Lecture Notes in Physics, 127, Springer, Berlin, 368-377. 
  36. [36] C. VOGT, 1982, A homogenization theorem leading to a Volterra integro-differential equation for permeation chromatography, Preprint 155, SFB 123, Universität Heidelberg. 

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