Reactive transport through an array of cells with semi-permeable membranes
ESAIM: Modélisation mathématique et analyse numérique, Tome 28 (1994) no. 1, pp. 59-94. 
@article{M2AN_1994__28_1_59_0,
     author = {Hornung, U. and J\"ager, W. and Mikeli\'c, A.},
     title = {Reactive transport through an array of cells with semi-permeable membranes},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {59--94},
     publisher = {AFCET - Gauthier-Villars},
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     volume = {28},
     number = {1},
     year = {1994},
     mrnumber = {1259268},
     zbl = {0824.76083},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1994__28_1_59_0/}
}
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Hornung, U.; Jäger, W.; Mikelić, A. Reactive transport through an array of cells with semi-permeable membranes. ESAIM: Modélisation mathématique et analyse numérique, Tome 28 (1994) no. 1, pp. 59-94. http://www.numdam.org/item/M2AN_1994__28_1_59_0/

[1] I. Aganović, A. Mikelić, 1992, Homogenization of nonstationary flow of a two-constituent mixture through a porous medium, Asymptotic Analysis, 6, 173-189. | MR | Zbl

[2] G. Allaire, 1989, Homogenization of the Stokes flow in a connected porous medium, Asympt. Anal, 2, 203-222. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[6] N. Bakhvalov, G. Panasenko, 1989, Homogenization : Averaging Processes in Periodic Media, Kluwer, Dordrecht. | MR | Zbl

[7] A. Bensoussan, J. L. Lions, G. Papanicolaou, 1978, Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam. | MR | Zbl

[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. | MR | Zbl

[9] A. P. Bourgeat, 1986, Homogenization of two-phase flow equations, Proceedings Symposia Pure Mathem., 45, 157-163. | MR | Zbl

[10] H. Brézis, 1972, Problèmes unilatéraux, J. Math. pures et appl., 51, 1-168. | MR | Zbl

[11] E. Canon, W. Jäger, Homogenization for nonlinear adsorption-diffusion processes in porous media, to appear.

[12] D. Cioranescu, J. Saint-Jean-Paulin, 1979, Homogenization in open sets with holes, J. Math. Anal. Appl., 71, 590-607. | MR | Zbl

[13] I. Ekeland, R. Temam, 1976, Convex Analysis and Variational Problems, North-Holland, Amsterdam. | MR | Zbl

[14] A. Friedman, P. Knabner, A Transport Model with Micro-and Macro-Structure, J. Differ. Equ., to appear. | Zbl

[15] K. Groger, 1971, Zum Rand-Anfangswertproblem der Adsorption und Diffusion bei Festbettprozessen, Mathem. Nachr., 49, 251-259. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | Zbl

[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. | MR

[20] U. Hornung, W. Jäger, 1991, Diffusion, convection, adsorption, and reaction of chemicals in porous media, J. Differ. Equat., 92, 199-225. | MR | Zbl

[21] U. Hornung, R. Showalter, 1990, Diffusion models for fractured media, J. Math. Anal. Applics, 147, 69-80. | MR | Zbl

[22] J. L. Lions, 1969, Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Dunod/Gauthier-Villars, Paris. | MR | Zbl

[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. | Zbl

[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. | MR | Zbl

[25] A. Mikelić, 1991, Homogenization of nonstationary Navier-Stokes equations in a domain with grained boundary, Ann, Mat. Pura e Appl., 158, 167-179. | MR | Zbl

[26] A. Mikelić, I. Aganović, 1987, Homogenization in a porous medium under a nonhomogeneous boundary condition, Boll. Un. Mat. Ital. (A) 1, 171-180. | MR | Zbl

[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. | MR | Zbl

[28] F. Murat, 1978, Compacité par compensation, Ann. Scuola Norm. Sup. Pisa, Ser. 4, 5, 489-507. | Numdam | MR | Zbl

[29] G. Nguetseng, 1989, A general convergence result for a functional related to the theory of homogenization, SIAM J. Math. Anal., 20, 608-623. | MR | Zbl

[30] O. A. Oleinik, S. M. Kozlov, V. V. Zhikov, 1991, Homogenization Differential Operators, North-Holland, Amsterdam.

[31] E. Sanchez-Palencia, 1980, Non-Homogeneous Media and Vibration Theory, Springer Lecture Notes in Physics, 129. | MR | Zbl

[32] K. Sattel-Schwind, 1988, Untersuchung über Diffusionsvorgänge bei der Gelpermeations-Chromatographie von Poly-p-Methylstyrol, Dissertation, Fachbereich Chemie, Universität Heidelberg.

[33] K. Siebel, 1988, Diffusion in dispersen Medien. Homogenisierung, Diplomarbeit Fachbereich Mathematik, Universitat Heidelberg.

[34] J. Simon, 1987, Compact sets in the space Lp(0, T ; B), Ann. Mat. Pura e Appl., 145, 65-96. | MR | Zbl

[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] C. Vogt, 1982, A homogenization theorem leading to a Volterra integro-differential equation for permeation chromatography, Preprint 155, SFB 123, Universität Heidelberg.