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Volumn 88, Issue 9, 2009, Pages 1265-1282

Homogenization of a pseudoparabolic system

Author keywords

Dynamic capillary pressure; Fractured porous media; Homogenization; Pseudoparabolic equations

Indexed keywords


EID: 70449134028     PISSN: 00036811     EISSN: 1563504X     Source Type: Journal    
DOI: 10.1080/00036810903277077     Document Type: Article
Times cited : (31)

References (39)
  • 1
    • 84926786894 scopus 로고    scopus 로고
    • The diffusion of imprisoned radiation through a gas
    • E. Milne, The diffusion of imprisoned radiation through a gas, J. London Math. Soc. 1 (1926), pp. 40-51.
    • J. London Math. Soc , vol.1 , Issue.1926 , pp. 40-51
    • Milne, E.1
  • 2
    • 36248938881 scopus 로고    scopus 로고
    • Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks (strata)
    • G.I. Barenblatt, I.P. Zheltov, and I.N. Kochina, Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks (strata), J. Appl. Math. Mech. 24 (1960), pp. 1286-1303.
    • J. Appl. Math. Mech , vol.24 , Issue.1960 , pp. 1286-1303
    • Barenblatt, G.I.1    Zheltov, I.P.2    Kochina, I.N.3
  • 3
    • 0006500336 scopus 로고    scopus 로고
    • On the problem of the process of propagation of heat in heterogeneous media
    • L.I. Rubenstein, On the problem of the process of propagation of heat in heterogeneous media, Izv. Akad. Nauk SSSR, Ser. Geogr. 1 (1948), pp. 12-45.
    • Izv. Akad. Nauk SSSR, Ser. Geogr , vol.1 , Issue.1948 , pp. 12-45
    • Rubenstein, L.I.1
  • 4
    • 0039633096 scopus 로고    scopus 로고
    • The final value problem for evolution equations
    • R.E. Showalter, The final value problem for evolution equations, J. Math. Anal. Appl. 47 (1974), pp. 563-572.
    • J. Math. Anal. Appl , vol.47 , Issue.1974 , pp. 563-572
    • Showalter, R.E.1
  • 5
    • 85121572269 scopus 로고    scopus 로고
    • Nonlinear inverse scale space methods
    • M. Burger, G. Gilboa, S. Osher, and J. Xu, Nonlinear inverse scale space methods, Commun. Math. Sci. 4 (2006), pp. 179-212.
    • Commun. Math. Sci , vol.4 , Issue.2006 , pp. 179-212
    • Burger, M.1    Gilboa, G.2    Osher, S.3    Xu, J.4
  • 6
    • 38949093647 scopus 로고    scopus 로고
    • A generalized eigenproblem for the Laplacian which arises in lightning
    • B.C. Aslan, W.W. Hager, and S. Moskow, A generalized eigenproblem for the Laplacian which arises in lightning, J. Math. Anal. Appl. 341 (2008), pp. 1028-1041.
    • J. Math. Anal. Appl , vol.341 , Issue.2008 , pp. 1028-1041
    • Aslan, B.C.1    Hager, W.W.2    Moskow, S.3
  • 7
    • 0002189557 scopus 로고    scopus 로고
    • Pseudoparabolic partial differential equations, SIAM
    • R.E. Showalter and T.W. Ting, Pseudoparabolic partial differential equations, SIAM J. Math. Anal. 1 (1970), pp. 1-26.
    • J. Math. Anal , vol.1 , Issue.1970 , pp. 1-26
    • Showalter, R.E.1    Ting, T.W.2
  • 8
    • 84972538756 scopus 로고    scopus 로고
    • Partial differential equations of Sobolev-Galpern type, Pacific
    • R.E. Showalter, Partial differential equations of Sobolev-Galpern type, Pacific J. Math. 31 (1969), pp. 787-793.
    • J. Math , vol.31 , Issue.1969 , pp. 787-793
    • Showalter, R.E.1
  • 9
    • 84972545547 scopus 로고    scopus 로고
    • Parabolic and pseudo-parabolic partial differential equations
    • T.W. Ting, Parabolic and pseudo-parabolic partial differential equations, J. Math. Soc.Japan 21 (1969), pp. 440-453.
    • J. Math. Soc.Japan , vol.21 , Issue.1969 , pp. 440-453
    • Ting, T.W.1
  • 11
    • 0003608087 scopus 로고
    • Petroleum Publishing Company, Tulsa, 1976 (Originally published by Van Nostrand Reinhold
    • R. Collins, Flow of Fluids Through Porous Materials, Petroleum Publishing Company, Tulsa, 1976 (Originally published by Van Nostrand Reinhold, 1961).
    • (1961) Flow of Fluids Through Porous Materials
    • Collins, R.1
  • 13
    • 0000339436 scopus 로고    scopus 로고
    • Nonsteady flow of water and oil through inhomogeneous porous media
    • H.W. Alt and E. DiBenedetto, Nonsteady flow of water and oil through inhomogeneous porous media, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 12(4) (1985), pp. 335-392.
    • Ann. Scuola Norm. Sup. Pisa Cl. Sci , vol.12 , Issue.1985 , pp. 335-392
    • Alt, H.W.1    Dibenedetto, E.2
  • 14
    • 0000152709 scopus 로고    scopus 로고
    • On nonstationary flow through porous media
    • H. Alt, S. Luckhaus, and A. Visintin, On nonstationary flow through porous media, Ann. Mat. Pura Appl. 136 (1984), pp. 303-316.
    • Ann. Mat. Pura Appl , vol.136 , Issue.1984 , pp. 303-316
    • Alt, H.1    Luckhaus, S.2    Visintin, A.3
  • 15
    • 38249010485 scopus 로고    scopus 로고
    • The existence of weak solutions to single porosity and simple dualporosity models of two-phase incompressible flow
    • T. Arbogast, The existence of weak solutions to single porosity and simple dualporosity models of two-phase incompressible flow, Nonlinear Anal. 19 (1992), pp. 1009-1031.
    • Nonlinear Anal , vol.19 , Issue.1992 , pp. 1009-1031
    • Arbogast, T.1
  • 16
    • 0027881895 scopus 로고    scopus 로고
    • Thermodynamic basis of capillary pressure on porous media
    • S. Hassanizadeh and W.G. Gray, Thermodynamic basis of capillary pressure on porous media, Water Resour. Res. 29 (1993), pp. 3389-3405.
    • Water Resour. Res , vol.29 , Issue.1993 , pp. 3389-3405
    • Hassanizadeh, S.1    Gray, W.G.2
  • 17
    • 0346198369 scopus 로고    scopus 로고
    • A mathematical model of non-equilibrium counter-current capillary imbibition
    • G. Barenblatt and A.A. Gil'man, A mathematical model of non-equilibrium counter-current capillary imbibition, J. Eng. Phys. 52 (1987), pp. 456-461.
    • J. Eng. Phys , vol.52 , Issue.1987 , pp. 456-461
    • Barenblatt, G.1    Gil'man, A.A.2
  • 18
    • 0346009268 scopus 로고    scopus 로고
    • The mathematical model of non-equilibrium effects in water-oil displacement
    • G.I. Barenblatt, D.B. Silin, and T.W. Patzek, The mathematical model of non-equilibrium effects in water-oil displacement, SPEJ 8 (2003), pp. 409-416.
    • SPEJ , vol.8 , Issue.2003 , pp. 409-416
    • Barenblatt, G.I.1    Silin, D.B.2    Patzek, T.W.3
  • 19
    • 83455218430 scopus 로고    scopus 로고
    • Dynamic effects in the capillary pressure saturation relationship and their impacts on unsaturated flow
    • S. Hassanizadeh, M. Celia, and H. Dahle, Dynamic effects in the capillary pressure saturation relationship and their impacts on unsaturated flow, Vadose Zone J. 1 (2002), pp. 38-57.
    • (2002) Vadose Zone J , vol.1 , pp. 38-57
    • Hassanizadeh, S.1    Celia, M.2    Dahle, H.3
  • 20
    • 0032949902 scopus 로고    scopus 로고
    • Laboratory investigations of effective flow behavior in unsaturated heterogeneous sands
    • D. Wildenschild and K. Jensen, Laboratory investigations of effective flow behavior in unsaturated heterogeneous sands, Water Res. Res. 35 (1999), pp. 17-27.
    • Water Res. Res , vol.35 , Issue.1999 , pp. 17-27
    • Wildenschild, D.1    Jensen, K.2
  • 21
    • 24644495883 scopus 로고    scopus 로고
    • Quantitative analysis of flow processes in a sand using synchrotron-based X-ray microtomography
    • D. Wildenschild, J. Hopmans, A. Kent, and M. Rivers, Quantitative analysis of flow processes in a sand using synchrotron-based X-ray microtomography, Vadose Zone J. 4 (2005), pp. 112-126.
    • Vadose Zone J , vol.4 , Issue.2005 , pp. 112-126
    • Wildenschild, D.1    Hopmans, J.2    Kent, A.3    Rivers, M.4
  • 22
    • 0035109062 scopus 로고    scopus 로고
    • Flow rate dependence of soil hydraulic characteristics
    • D. Wildenschild, J.W. Hopmanns, and J. Simunek, Flow rate dependence of soil hydraulic characteristics, Soil Sci. Soc. Am. J. 65 (2001), pp. 35-48.
    • Soil Sci. Soc. Am. J , vol.65 , Issue.2001 , pp. 35-48
    • Wildenschild, D.1    Hopmanns, J.W.2    Simunek, J.3
  • 23
    • 0032446093 scopus 로고    scopus 로고
    • Effective two-phase flow through highly heterogeneous porous media: Capillary nonequilibrium effects
    • A. Bourgeat and M. Panfilov, Effective two-phase flow through highly heterogeneous porous media: Capillary nonequilibrium effects, Comput. Geosci. 2 (1998), pp. 191-215.
    • Comput. Geosci , vol.2 , Issue.1998 , pp. 191-215
    • Bourgeat, A.1    Panfilov, M.2
  • 24
    • 56649088279 scopus 로고    scopus 로고
    • Numerical methods for unsaturated flow with dynamic capillary pressure in heterogeneous porous media
    • M. Peszyńska and S.Y. Yi, Numerical methods for unsaturated flow with dynamic capillary pressure in heterogeneous porous media, Int. J. Numer. Anal. Model. 5 (2008), pp. 126-149.
    • Int. J. Numer. Anal. Model , vol.5 , Issue.2008 , pp. 126-149
    • Peszyńska, M.1    Yi, S.Y.2
  • 25
    • 83455218430 scopus 로고    scopus 로고
    • Dynamic effect in the capillary pressure saturation relationship and its impacts on unsaturated flow
    • S.M. Hassanizadeh, M. Celia, and H. Dahle, Dynamic effect in the capillary pressure saturation relationship and its impacts on unsaturated flow, Vadose Zone J. 1 (2002), pp. 38-57.
    • Vadose Zone J , vol.1 , Issue.2002 , pp. 38-57
    • Hassanizadeh, S.M.1    Celia, M.2    Dahle, H.3
  • 26
    • 33846650565 scopus 로고    scopus 로고
    • Diffusion in fissured media
    • M. Böhm and R.E. Showalter, Diffusion in fissured media, SIAM J. Math. Anal. 16 (1985), pp. 500-509.
    • SIAM J. Math. Anal , vol.16 , Issue.1985 , pp. 500-509
    • Böhm, M.1    Showalter, R.E.2
  • 27
    • 0016028311 scopus 로고    scopus 로고
    • Degenerate evolution equations and applications
    • R.E. Showalter, Degenerate evolution equations and applications, Indiana Univ. Math. J. 23 (1973/74), pp. 655-677.
    • Indiana Univ. Math. J , vol.23 , Issue.1973-1974 , pp. 655-677
    • Showalter, R.E.1
  • 34
    • 0001085153 scopus 로고    scopus 로고
    • Derivation of the double porosity model of single phase flow via homogenization theory
    • T. Arbogast, J. Douglas Jr, and U. Hornung, Derivation of the double porosity model of single phase flow via homogenization theory, SIAM J. Math. Anal. 21 (1990), pp. 823-836.
    • SIAM J. Math. Anal , vol.21 , Issue.1990 , pp. 823-836
    • Arbogast, T.1    Douglas Jr., J.2    Hornung, U.3
  • 35
    • 21144473666 scopus 로고    scopus 로고
    • Homogenization and two-scale convergence
    • G. Allaire, Homogenization and two-scale convergence, SIAM J. Math. Anal. 23 (1992), pp. 1482-1518.
    • SIAM J. Math. Anal , vol.23 , Issue.1992 , pp. 1482-1518
    • Allaire, G.1
  • 36
    • 0002993483 scopus 로고    scopus 로고
    • Two-scale convergence of a model for flow in a partially fissured medium
    • G.W. Clark and R.E. Showalter, Two-scale convergence of a model for flow in a partially fissured medium, Electron. J. Differ. Equ. 1999(2) (1999), pp. 1-20.
    • (1999) Electron. J. Differ. Equ , vol.1999 , Issue.2 , pp. 1-20
    • Clark, G.W.1    Showalter, R.E.2
  • 37
    • 84972505066 scopus 로고    scopus 로고
    • On a model of nonisothermal flow through fissured media
    • M. Peszyńska, On a model of nonisothermal flow through fissured media, Differ. Integral Equ. 8 (1995), pp. 1497-1516.
    • Differ. Integral Equ , vol.8 , Issue.1995 , pp. 1497-1516
    • Peszyńska, M.1
  • 39
    • 38149024039 scopus 로고    scopus 로고
    • Effective equations for two-phase flow in porous media: The effect of trapping on the microscale
    • C.J. van Duijn, H. Eichel, R. Helmig, and I.S. Pop, Effective equations for two-phase flow in porous media: The effect of trapping on the microscale, Transp. Porous Media 69 (2007), pp. 411-428.
    • Transp. Porous Media , vol.69 , Issue.2007 , pp. 411-428
    • van Duijn, C.J.1    Eichel, H.2    Helmig, R.3    Pop, I.S.4


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