Compressible flow in fractured porous media with an unbounded density-pressure law

References

• Adler , P.M. 1992 . “ Porous Media ” . In Geometry and Transport , Boston, , London, Wellington : Butterworth-Heinemann .
   Google Scholar
• Arbogast , T. 1989 . The double Porosity Model for Single Phnre Flow through a Naturally Fractured Reservoir . SIAM. J. Num. Anal. , 26 ( 1 ) : 12 – 29 .
   Web of Science ®Google Scholar
• Arbogast , T. and Douglas , J. 1990 . “ Dual Porosity Models for Flows in Naturally Fractured Reservoirs ” . In Dynamics of Fluids in Hierarchical Porous Media , Edited by: Cushman , J.J. 177 – 221 . Acd. Pr. .
   Google Scholar
• Arhogast , T. , Hornung , U. and Douglns , J. 1990 . Derivation of the Double Porosity Model of Single Phase Flow via Houiogeuization Theory . SIAM J . Matheni. Anal. , 212 ( 4 ) : 823 – 826 .
   Google Scholar
• Barenblatt , G.I. , Entov , V.M. and Ryzhik , V.M. 1990 . Theory of flows through Natural Rocks , Dordrecht/Boston/London : Kluwer Acatl. Publ. .
   Google Scholar
• Barenblatt , G.I. , Zheltov , Y.P. and Kochina , I.N. 1960 . Basic concepts in the theory of seepage flow of homogeneous liquids in fissured rocks . J. Appl. Math. and Mech. , 24 : 1286 – 1303 .
   Google Scholar
• Bear , J. and Bachmat , Y. 1990 . Introduction to Motleling of Transport Phenomena in Porous Media , Dordrecht/Boston/London : Kluwer Acad. Publ. .
   Google Scholar
• Böhm M. in preparation
   Google Scholar
• Bölun , M. and Showalter , R. E. 1985 . Diffusion in Fissured Media . SIAM J. Math. Anal. , 16 ( 3 ) : 500 – 519 .
   Google Scholar
• Bö M. Compressible Flow in Fractured Porous Media with an Unbounded Density-Pressure Law, CAMS-report Univ. of Southern California at Los Angels 1995 extended version of this paper, including a derivation of the model.
   Google Scholar
• Bourgeat , A. and Hidani , A. 1995 . A Result of Existence for a Model of Two-Phase Flow in a Porous Medium made of Different Rock Types . Appl. Analysis , 56 ( 4 ) : 381 – 399 .
   Google Scholar
• Brézis , H. and Strams , W. 1973 . Semi-linear second order elliptic equations in L1 . Journ. Math. Soc. Japan , 25 ( 4 )
   Google Scholar
• Carroll , R.W. and Showalter , K.E. 1976 . “ Singular antl degenerate Canclly Problems ” . In Mathematics in Science antl Engineering Vol. 127 , New York, , London : Academic Pr., .
   Google Scholar
• DaPrato , G. Applications croissantes et éqations d'éevolution dans les espaces tle Banach , New York, , London : Acad. Pr. .
   Google Scholar
• DiBenetletto , E. and Showalter , R.E. 1982 . A Pseudo-Paral)olic Variational Inequality antl Stefan Problem . Nonlinear Analysis - Theory, Methods & Application , 6 ( 3 ) : 279 – 291 .
   Web of Science ®Google Scholar
• DiBenedetto , E. and Pierre , M. 1981 . On the maximum principle for pseudo-parabolic equations . Indiana Univ. Journ. , 30 ( 6 ) Nov-Dec
   Google Scholar
• Douglas , J. , Hensley , J.L. and Leme , P.J.P. 1993 . “ A study of the effect of inhomogeneities on immiscible flow in naturally fractured Reservoirs ” . In Flow in Porous Media , Edited by: Douglas , J. Basel-Berlin-Boston : Birkhäuser Verlag .
   Google Scholar
• Ene , H.I. 1990 . “ Applicaton of the Ilomogenization Method to Transport in Porous Media ” . In Dynamics of Fluitls in Hierarcllical Porous Media , Edited by: Cushman , J.H. 223 – 241 . Acad. Pr. .
   Google Scholar
• Favini , A. and Plazzi . 1992 . On some abstract degenerate prolblems of pseudo-parabolic type . J. Applications to linear and nonlinear problems , preprint
   Google Scholar
• Favini , A. and Yagi , A. Multivalued linear operators and degenerate evolution equations . preprint, to appear in Annali tli Mat. ,
   Google Scholar
• Gajewski , H. , Gröger , K. and Zacharias , K. 1974 . Nichtlineare Operatorgleichungen und Operatordifferntialgleichungen , Berlin : Akademie-Verlag .
   Google Scholar
• Gilbarg , D. and Trutlinger , N. 1983 . Elliptic Partial Differential Equations of second order , Berlin-New York : Springer Verlag .
   Google Scholar
• Griepenberg , C. , Londen , S.-0. and Staffans , 0. 1990 . Volterra-Integral and Functional Equations , Cambridge University Press .
   Google Scholar
• Gröger , K. and Rehberg , J. 1989 . Resolvent Estimates in W1,p for order elliptic differential operators in case of mixed boundary conditions . Mathem. Ann. , 285 : 105 – 113 .
   Google Scholar
• Hornung , U. 1991 . Miscible Displacement in Porous Media influenced by Mobile and Immobile Water . Rocky mountain Journ. of Mathem. , 22 ( 2 ) : 645 – 669 . Spring
   Google Scholar
• Hournung , U. and R.E.Showalter . 1990 . Diffusion Models for Fractured Media . Journ. Math. Anal. Appl , 147 : 69 – 80 .
   Google Scholar
• Kufner , A. , John , O. and Fucik , S. 1970 . Function Spaces . Academia Prague ,
   Google Scholar
• Kuttler , K.L. 1984 . Time dependent implicit evolution equations . Nonlin. Analysis. Theory Methods & Applications , 10 ( 5 ) : 447 – 463 .
   Web of Science ®Google Scholar
• Meyers , N. 1963 . An Lp-estimate for the gradient of second order elliptic equations in divergence form . Ann. Scuola Norm. Sup. Pisa, Ser.III , XVII : 189 – 206 .
   Google Scholar
• Peszynska , M. 1992 . Flow through Fissured Media . Innaugural Dissertation, Augsburg ,
   Google Scholar
• Runtlell , W. and Stecher , M. 1978 . The nonpositivity of solutions to pseudoparabolic equations . Proc. Amer. Mathem. Soc. , 75 ( 2 )
   Web of Science ®Google Scholar
• Showalter , R.E. and Walkington , N.J. 1991 . Diffusion of Fluid in a Fissured Medium with Mi- crostructure . SIAM Journ. Math. Analysis , 22 ( 6 ) : 1702 – 1722 .
   Web of Science ®Google Scholar
• Showalter , R.E. 1993 . “ Distributed Microstructure Models of Porous Media ” . In Flow in Porous Media, International Series of Numerical Mathematics , Edited by: Douglas , J. and Hornung , U. Basel-Berlirl-Boston : Birkhäuser Verlag .
   Google Scholar
• Simader , Chr. 1972 . “ On Dirichlet's Boundary Value Problem ” . In Lecture Notes Mathem. Nr. , Vol. 268 , Berlin-New York : Springer-Verlag .
   Google Scholar
• Stampacchia , G. 1963 . Some limit cases of Lp-estimates for solutions of second order elliptic equations . Comm. Pure and Appl. Mathem. , XVI : 505 – 510 .
   Google Scholar
• Sviridjuk , G.A. 1993 . “ Studies on Semi-Linear Equations of Sobolev-type in Banach-spaces ” . In survey and halbilitation , dekaterinburg, Russian : Russian Acatl. of Science .
   Google Scholar
• Sviridjuk , G.A. and Apetova , T.A. 1993 . Phase Spaces of Linear Time Dependent Equations of Sobolev-type . Proc. of the Russiau Acatl. of Science , 330 ( 6 ) : 696 – 699 . Dokl. Acad. Nauk
   Web of Science ®Google Scholar