Modeling and homogenizing a problem of absorption/desorption in porous media

Mathematical Models and Methods in Applied Sciences

Volumn 16, Issue 11, 2006, Pages 1751-1781

  Mikelić, Andro ^a   Primicerio, Mario ^b  

^a UNIVERSITÉ LYON 1   (France)

^b Dipartimento di Matematica U Dini   (Italy)

Author keywords

Absorption in porous media; Homogenization; Nonlinear chemical kinetics; Nonlinear parabolic PDEs

Indexed keywords

EID: 33750689165     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202506001704     Document Type: Article

References (24)

1. G. Allaire and F. Murat, Homogenization of the Neumann problem with nonisolated holes, Asympt. Anal. 7 (1993) 81-95.
2. G. Allaire, A. Damlamian and U. Hornung, Two-scale convergence on periodic surfaces and applications, in Mathematical Modelling of Flow through Porous Media (World Scientific, 1995), pp. 15-25.
3. J. Bear and A. Verruijt, Modeling Groundwater Flow and Pollution (D. Reidel, 1987).
4. M. Briane, Homogenization of the torsion problem and the Neumann problem in nonregular periodically perforated domains, Math. Mod. Meth. Appl. Sci. 7 (1997) 847-870.
5. D. Cioranescu and J. Saint Jean Paulin, Homogenization in open sets with holes, J. Math. Anal. Appl. 71 (1979) 590-607.
6. D. Cioranescu and P. Donato, Homogénéisation du problème de Neumann nonhomogène dans des ouverts perforés, Asympt. Anal. 1 (1988) 115-138.
7. C. Conca, J. I. Diaz, A. Liñán and C. Timofte, Homogenization in chemical reactive flows through porous media, Electron. J. Diff. Eqns. (2004), paper 40.
8. C. Conca, J. I. Diaz and C. Timofte, Effective chemical processes in porous media, Math. Mod. Meth. Appl. Sci. 13 (2003) 1437-1462.
9. A. Friedman, Partial Differential Equations of Parabolic Type (Prentice-Hall, 1964).
10. A. Friedman and P. Knabner, A transport model with micro- and macro-structure, J. Diff. Eqns. 98 (1992) 328-354.
11. D. W. Hendricks, Sorption in flow through porous media, in Fundamentals of Transport Phenomena in Porous Media, ed. J. Bear (Elsevier, 1972), pp. 384-392.
12. D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, Vol. 840 (Springer-Verlag, 1993).
13. R. Hochmuth and P. Deuflhard, Multiscale analysis for the bio-heat transfer equations - the nonisolated case, Math. Mod. Meth. Appl. Sci. 14 (2004) 1621-1634.
14. U. Hornung and W. Jäger, Diffusion, convection, adsorption, and reaction of chemicals in porous media, J. Diff. Eqns. 92 (1991) 199-225.
15. U. Hornung, W. Jäger and A. Mikelić, Reactive transport through an array of cells with semi-permeable membranes, Model. Math. Anal. Numér. 28 (1994) 59-94.
16. V. V. Jikov, S. M. Kozlov and O. A. Oleinik, Homogenization of Differential Operators and Integral Functionals (Springer-Verlag, 1994).
17. O. A. Ladyženskaya, V. A. Solonnikov and N. N. Ural'ceva, Linear and Quasi-Linear Equations of Parabolic Type, Translations of Mathematical Monographs, Vol. 23 (Amer. Math. Soc., 1968).
18. A. Mikelić and M. Primicerio, Homogenization of a problem modelling remediation of porous media, Far East J. Appl. Math. 15 (2004) 365-380.
19. A. Mikelić and M. Primicerio, Oxygen exchange between multiple capillaries and living tissues: A homogenization study, Rend. Mat. Acc. Lincei 13 (2002) 149-164.
20. A. Mikelić and M. Primicerio, A diffusion-consumption problem for oxygen in a living tissue perfused by capillaries, Nonlinear Diff. Eqns. Appl. 13 (2006), in press.
21. M. Neuss-Radu, Some extensions of two-scale convergence, C. R. Acad. Sci. Paris Sér. I Math. 322 (1996) 899-904.
22. C. V. Pao, Stability analysis of a coupled diffusion-transport system for oxygen transport in blood and tissue, Nonl. Anal. Th. Met. Appl. 9 (1985) 1037-1059.
23. J. Rubin, Transport of reacting solutes in porous media: Relation between mathematical nature of problem formulation and chemical nature of reactions, Water Res. Res. 19 (1983) 1231-1252.
24. M. Th. van Genuchten, Mass transfer studies of sorbing porous media, Ph.D. Thesis, New Mexico State University, La Cruz, USA, 1974.