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Homogenization of a dual-permeability problem in two-component media with imperfect contact. (English) Zbl 1363.35021
The author considers as microscopic problem a weakly coupled system of Darcy-like equations for slightly compressible flows, posed for fluid velocities through a high-contrast periodic media. The system is linked via transmission conditions of Deresiewicz-Skalak type. The target of this paper - the derivation of a single macroscopic pressure model - is reached by a fine application of two-scale convergence arguments for a particular scaling of the microscopic model in terms of the small parameter \(\epsilon\). The choice of scaling describes what the author means by a high contrast in two microstructural phases that have an imperfect contact.

MSC:
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
76S05 Flows in porous media; filtration; seepage
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References:
[1] Ainouz, A., Homogenized double porosity models for poro-elastic media with interfacial flow barrier, Math. Bohem., 136, 357-365, (2011) · Zbl 1249.35016
[2] Ainouz, A., Homogenization of a double porosity model in deformable media, Electron. J. Differ. Equ., 2013, 1-18, (2013) · Zbl 1365.05013
[3] Allaire, G., Homogenization and two-scale convergence, SIAM J. Math. Anal., 23, 1482-1518, (1992) · Zbl 0770.35005
[4] Allaire, G.; Damlamian, A.; Hornung, U.; Bourgeat, A. (ed.); etal., Two-scale convergence on periodic surfaces and applications, 15-25, (1995), Singapore
[5] Arbogast, T.; Douglas, J.; Hornung, U., Derivation of the double porosity model of single phase flow via homogenization theory, SIAM J. Math. Anal., 21, 823-836, (1990) · Zbl 0698.76106
[6] A. Bensoussan, J.-L. Lions, G. Papanicolaou: Asymptotic Analysis for Periodic Structures. Studies in Mathematics and its Applications 5, North-Holland Publ. Company, Amsterdam, 1978. · Zbl 0404.35001
[7] Clark, G. W., Derivation of microstructure models of fluid flow by homogenization, J. Math. Anal. Appl., 226, 364-376, (1998) · Zbl 0927.35081
[8] Deresiewicz, H.; Skalak, R., On uniqueness in dynamic poroelasticity, Bull. Seismol. Soc. Amer., 53, 783-788, (1963)
[9] Ene, H. I.; Poliševski, D., Model of diffusion in partially fissured media, Z. Angew. Math. Phys., 53, 1052-1059, (2002) · Zbl 1017.35016
[10] Rohan, E.; Naili, S.; Cimrman, R.; Lemaire, T., Multiscale modeling of a fluid saturated medium with double porosity: relevance to the compact bone, J. Mech. Phys. Solids, 60, 857-881, (2012)
[11] E. Sanchez-Palencia: Non-Homogeneous Media and Vibration Theory. Lecture Notes in Physics 127, Springer, Berlin, 1980. · Zbl 0432.70002
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