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Original Articles

Upscaling nonlinear adsorption in periodic porous media – homogenization approach

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Pages 2126-2161 | Received 06 Jan 2015, Accepted 02 Apr 2015, Published online: 27 Apr 2015

References

  • Taylor GI. Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. Royal Soc. A. 1953;219:186–203.
  • Hornung U, editor. Homogenization and porous media, interdisciplinary applied mathematics. Vol. 6. New York (NY): Springer-Verlag; 1997.
  • Jikov VV, Kozlov SM, Oleinik OA. Homogenization of differential operators and integral functionals. Berlin: Springer; 1994.
  • Auriault J-L, Adler P-M. Taylor dispersion in porous media: analysis by multiple scale expansions. Adv. Water Res. 1995;18:17–226.
  • Choquet C, Mikelić A. Laplace transform approach to the rigorous upscaling of the infinite adsorption rate reactive flow under dominant Peclet number through a pore. Appl. Anal. 2008;87:1373–1395.
  • Conca C, Diaz JI, Timofte C. Effective chemical processes in porous media. Math. Models Methods Appli. Sci. 2003;13:1437–1462.
  • van Duijn CJ, Knabner P. Travelling waves in the transport of reactive solutes through porous media: Adsorption and binary ion exchange–part 1. Transp. Porous Media. 1992;8:167–194.
  • Hornung U, Jäger W. Diffusion, convection, adsorption, and reaction of chemicals in porous media. J. Differ. Equ. 1991;92:199–225.
  • Mauri R. Dispersion, convection, and reaction in porous media. Phys. Fluids A. 1991;3:743–756.
  • Mikelić A, Devigne V, van Duijn CJ. Rigorous upscaling of the reactive flow through a pore, under dominant Peclet and Damkohler numbers. SIAM J. Math. Anal. 2006;38:1262–1287.
  • Mikelić A, Primicerio M. Homogenization of a problem modeling remediation of porous media. Far East J. Appl. Math. 2004;15:365–380.
  • Mikelić A, Primicerio M. Modeling and homogenizing a problem of absorption/desorption in porous media. Math. Models Methods Appl. Sci. 2006;16:1751–1781.
  • Allaire G, Brizzi R, Mikelić A, Piatnitski A. Two-scale expansion with drift approach to the Taylor dispersion for reactive transport through porous media. Chem. Eng. Sci. 2010;65:2292–2300.
  • Allaire G, Hutridurga H. Homogenization of reactive flows in porous media and competition between bulk and surface diffusion. IMA J. Appl. Math. 2012;77:788–815.
  • Allaire G, Mikelić A, Piatnitski A. Homogenization approach to the dispersion theory for reactive transport through porous media. SIAM J. Math. Anal. 2010;42:125–144.
  • Hornung U, Jäger W, Mikelić A. Reactive transport through an array of cells with semipermeable membranes. M2AN. 1994;28:59–94.
  • Allaire G, Hutridurga H. On the homogenization of multicomponent transport. Submitted. arxiv:1411.5317.
  • Marusic-Paloka E, Piatnitski A. Homogenization of a nonlinear convection-diffusion equation with rapidly oscillating coefficients and strong convection. J. London Math. Soc. 2005;72:391–409.
  • Allaire G, Piatnitski A. Homogenization of nonlinear reaction-diffusion equation with a large reaction term. Annali dell’Universita di Ferrara. 2010;56:141–161.
  • Allaire G. Periodic homogenization and effective mass theorems for the Schrödinger equation. In: Ben Abdallah N, Frosali G, editors. Quantum transport-modelling, analysis and asymptotics. Lecture notes in mathematics 1946. Berlin: Springer; 2008. p. 1–44.
  • Hutridurga H. Homogenization of complex flows in porous media and applications [doctoral thesis]. Palaiseau: Ecole Polytechnique; 2013.
  • Protter MH, Weinberger HF. Maximum principles in differential equations. New York (NY): Springer-Verlag; 1984.
  • Ladyzhenskaya OA, Solonikov VA, Ural’ceva NN. Linear and quasilinear equations of parabolic type. Providence (RI): American Mathematical Society; 1968.
  • Lions J-L. Quelques méthodes de résolution des problèmes aux limites non linéaires [Some methods for solving nonlinear boundary value problems]. Paris: Dunod; Gauthier-Villars; 1969.
  • Cioranescu D, Saint Jean Paulin J. Homogenization in open sets with holes. J. Math. Anal. Appl. 1979;71:590–607.
  • Acerbi E, Chiado Piat V, Dal Maso G, Percivale D. An extension theorem from connected sets, and homogenization in general periodic domains. Nonlinear Anal. 1992;18:481–496.
  • Brézis H. Analyse Fonctionelle, Théorie et applications. Collection Mathématiques Appliquées pour la Maîtrise [Theory and applications. Collection of applied mathematics for the Master’s Degree]. Paris: Masson; 1983.
  • Amaziane B, Pankratov L, Piatnitski A. Homogenization of immiscible compressible two-phase flow in highly heterogeneous porous media with discontinuous capillary pressures. M3AS. 2014;24:1421–1451.
  • Allaire G. Homogenization and two-scale convergence. SIAM J. Math. Anal. 1992;23:1482–1518.
  • Nguetseng G. A general convergence result for a functional related to the theory of homogenization. SIAM J. Math. Anal. 1989;20:608–623.
  • Allaire G, Damlamian A, Hornung U. Two-scale convergence on periodic surfaces and applications. In: Bourgeat A, Carasso C, Mikelic A, Luckhaus S, editors. Proceedings of the International Conference on Mathematical Modelling of Flow through Porous Media (May 1995). Singapore: World Scientific Publishing Company; 1996. p. 15–25.
  • Neuss-Radu M. Some extensions of two-scale convergence. C.R. Acad. Sci. Paris Sr. I Math. 1996;322:899–904.
  • Allaire G, Orive R. Homogenization of periodic non self-adjoint problems with large drift and potential. COCV. 2007;13:735–749.
  • Brahim-Otsmane S, Francfort G, Murat F. Correctors for the homogenization of the wave and heat equations. J. Math. Pures Appl. 1992;71:97–231.

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