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Volumn 150, Issue 4, 1999, Pages 349-367

On the Barenblatt model for non-equilibrium two phase flow in porous media

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EID: 0033266226     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002050050191     Document Type: Article
Times cited : (13)

References (35)
  • 4
    • 0039280826 scopus 로고
    • Flow of two immiscible fluids in homogeneous porous medium
    • G. I. BARENBLATT, Flow of two immiscible fluids in homogeneous porous medium (in Russian) Izv. AN SSSR, Mekh. Zhidk. i Gaza, 5 (1971), 144-151.
    • (1971) Izv. AN SSSR, Mekh. Zhidk. i Gaza , vol.5 , pp. 144-151
    • Barenblatt, G.I.1
  • 6
    • 0002449293 scopus 로고
    • Non equilibrium seepage of immiscible fluids
    • G. I. BARENBLATT & A. P. VINNITCHENKO, Non equilibrium seepage of immiscible fluids (in Russian), Uspekhi Mekhaniki 3 (1980), 35-50.
    • (1980) Uspekhi Mekhaniki , vol.3 , pp. 35-50
    • Barenblatt, G.I.1    Vinnitchenko, A.P.2
  • 7
    • 85065356856 scopus 로고    scopus 로고
    • Mathematical model of the non-equilibrium water-oil displacement in porous strata
    • G. I. BARENBLATT, J. GARCIA-AZORERO, A. DE PABLO & J. L. VAZQUEZ, Mathematical model of the Non-equilibrium water-oil displacement in porous strata, Appl. Anal. 65 (1997), 19-45.
    • (1997) Appl. Anal. , vol.65 , pp. 19-45
    • Barenblatt, G.I.1    Garcia-Azorero, J.2    De Pablo, A.3    Vazquez, J.L.4
  • 8
    • 0000626041 scopus 로고
    • Mechanism of fluid displacement in sands
    • S. E. BUCKLEY & M. C. LEVERETT, Mechanism of fluid displacement in sands, Trans. AIME 142 (1942), 107-116.
    • (1942) Trans. AIME , vol.142 , pp. 107-116
    • Buckley, S.E.1    Leverett, M.C.2
  • 9
    • 84990689276 scopus 로고
    • Hyperbolic conservation laws with stiff relaxation terms and entropy
    • G.-Q. CHEN, C. LEVERMORE & T. P. LIU, Hyperbolic conservation laws with stiff relaxation terms and entropy, Comm. Pure Appl. Math. 47 (1994), 787-830.
    • (1994) Comm. Pure Appl. Math. , vol.47 , pp. 787-830
    • Chen, G.-Q.1    Levermore, C.2    Liu, T.P.3
  • 10
    • 0041059699 scopus 로고
    • Il problema di darboux per un'equazione di tipo iperbolico in due variabili
    • C. CILIBERTO, Il Problema di Darboux per un'equazione di tipo iperbolico in due variabili, Ricerche di Mat. 4 (1955), 15-29.
    • (1955) Ricerche di Mat. , vol.4 , pp. 15-29
    • Ciliberto, C.1
  • 13
    • 0040465546 scopus 로고
    • Sull'equazione integrodifferenziale di Darboux-Picard
    • R. CONTI, Sull'equazione integrodifferenziale di Darboux-Picard, Le Matematiche 13 (1958), 30-39.
    • (1958) Le Matematiche , vol.13 , pp. 30-39
    • Conti, R.1
  • 14
    • 84966243152 scopus 로고
    • Some relations between nonexpansive and order preserving mappings
    • M. G. CRANDALL & L. TARTAR, Some relations between nonexpansive and order preserving mappings, Proc. Amer. Math. Soc. 78 (1980), 385-390.
    • (1980) Proc. Amer. Math. Soc. , vol.78 , pp. 385-390
    • Crandall, M.G.1    Tartar, L.2
  • 16
    • 0003450356 scopus 로고
    • Frontiers in Applied Mathematics, 1. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
    • R. E. EWING (Ed.), The mathematics of reservoir simulation, Frontiers in Applied Mathematics, 1. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1983.
    • (1983) The Mathematics of Reservoir Simulation
    • Ewing, R.E.1
  • 18
    • 0039280823 scopus 로고
    • Sur un problème relatif à la théorie des équations aux dérivées partielles du second ordre, i mém
    • E. GOURSAT, Sur un problème relatif à la théorie des équations aux dérivées partielles du second ordre, I Mém., Annales de Toulouse (II) 5 (1903), 405-436.
    • (1903) Annales de Toulouse (II) , vol.5 , pp. 405-436
    • Goursat, E.1
  • 19
    • 0000364772 scopus 로고
    • On hyperbolic partial differential equations
    • PH. HARTMAN & A. WINTNER, On hyperbolic partial differential equations, American J.Math. 74 (1952), 834-864.
    • (1952) American J.Math. , vol.74 , pp. 834-864
    • Hartman, Ph.1    Wintner, A.2
  • 20
    • 0000282942 scopus 로고    scopus 로고
    • Contractive relaxation systems and the scalar multidimensional conservation law
    • M. A. KATSOULAKIS & A. E. TZAVARAS, Contractive relaxation systems and the scalar multidimensional conservation law, Comm. Partial Differential Equations 22 (1997), 195-223.
    • (1997) Comm. Partial Differential Equations , vol.22 , pp. 195-223
    • Katsoulakis, M.A.1    Tzavaras, A.E.2
  • 21
    • 84956238079 scopus 로고
    • First order quasilinear equations in several independent variables
    • S. N. KRUŽKOV, First order quasilinear equations in several independent variables, Math. USSR-Sb. 10 (1970), 217-243. Translation of: Mat. Sb. 81 (1970), 228-255.
    • (1970) Math. USSR-Sb. , vol.10 , pp. 217-243
    • Kružkov, S.N.1
  • 22
    • 84956238079 scopus 로고
    • S. N. KRUŽKOV, First order quasilinear equations in several independent variables, Math. USSR-Sb. 10 (1970), 217-243. Translation of: Mat. Sb. 81 (1970), 228-255.
    • (1970) Translation of: Mat. Sb. , vol.81 , pp. 228-255
  • 24
    • 0000895887 scopus 로고
    • Flow of oil-water mixture through unconsolidated sands
    • M. C. LEVERETT, Flow of oil-water mixture through unconsolidated sands, Trans. AIME 32 (1939), 149-171.
    • (1939) Trans. AIME , vol.32 , pp. 149-171
    • Leverett, M.C.1
  • 25
    • 21544449601 scopus 로고
    • Hyperbolic conservation laws with relaxation
    • T. P. LIU, Hyperbolic conservation laws with relaxation, Comm. Math. Phys. 108 ( 1987), 153-175.
    • (1987) Comm. Math. Phys. , vol.108 , pp. 153-175
    • Liu, T.P.1
  • 26
    • 0040465544 scopus 로고
    • Sur les suites infinies de fonctions
    • P. MONTEL, Sur les suites infinies de fonctions, Ann. Ec. Norm. Sup. 24 (1907), 233-234.
    • (1907) Ann. Ec. Norm. Sup. , vol.24 , pp. 233-234
    • Montel, P.1
  • 27
    • 36849128854 scopus 로고
    • The flow of heterogeneous fluids
    • M. MUSKAT & M. MERES, The flow of heterogeneous fluids, Physics 7 (1936), 346-363.
    • (1936) Physics , vol.7 , pp. 346-363
    • Muskat, M.1    Meres, M.2
  • 28
    • 0030490070 scopus 로고    scopus 로고
    • Convergence to equilibrium for the relaxation approximations of conservation laws
    • R. NATALINI, Convergence to equilibrium for the relaxation approximations of conservation laws, Comm. Pure Appl. Math. 49 (1996), 795-823.
    • (1996) Comm. Pure Appl. Math. , vol.49 , pp. 795-823
    • Natalini, R.1
  • 29
    • 11544335821 scopus 로고    scopus 로고
    • A discrete kinetic approximation of entropy solutions to multidimensional scalar conservation laws
    • R. NATALINI, A discrete kinetic approximation of entropy solutions to multidimensional scalar conservation laws, J. Differential Equations 148 (1998), 292-317.
    • (1998) J. Differential Equations , vol.148 , pp. 292-317
    • Natalini, R.1
  • 30
    • 0003141624 scopus 로고    scopus 로고
    • Recent results on hyperbolic relaxation problems
    • Analysis of Systems of Conservation Laws, ed. H. FREISTÜHLER, Chapman & Hall/CRC
    • R. NATALINI, Recent results on hyperbolic relaxation problems, in Analysis of systems of conservation laws, ed. H. FREISTÜHLER, Monographs and Survey in Pure and Applied Mathematics 99, Chapman & Hall/CRC, 1999.
    • (1999) Monographs and Survey in Pure and Applied Mathematics , vol.99
    • Natalini, R.1
  • 32
    • 84916731959 scopus 로고
    • Sur les méthodes d'approximations successives dans la théorie des équations différentielles
    • G. DARBOUX 4ème partie, Gauthier-Villars et fils, Paris
    • E. PICARD, Sur les méthodes d'approximations successives dans la théorie des équations différentielles, in G. DARBOUX Leçons sur la théorie générale des surfaces, 4ème partie, Gauthier-Villars et fils, Paris, 1896.
    • (1896) Leçons sur la Théorie Générale des Surfaces
    • Picard, E.1
  • 33
    • 0031537812 scopus 로고    scopus 로고
    • On the rate of convergence to equilibrium for a system of conservation laws with a relaxation term
    • A. TVEITO & R. WINTHER, On the rate of convergence to equilibrium for a system of conservation laws with a relaxation term, SIAM J. Math. Anal. 28 (1997), 136-161.
    • (1997) SIAM J. Math. Anal. , vol.28 , pp. 136-161
    • Tveito, A.1    Winther, R.2
  • 34
    • 0032362176 scopus 로고    scopus 로고
    • Asymptotic limit of the initial boundary value problems for conservation laws with relaxation extensions
    • W. C. WANG & Z. XIN, Asymptotic limit of the initial boundary value problems for conservation laws with relaxation extensions, Comm. Pure Appl. Math. 51 (1998), 505-535.
    • (1998) Comm. Pure Appl. Math. , vol.51 , pp. 505-535
    • Wang, W.C.1    Xin, Z.2


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