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Applicable Analysis
An International Journal
Volume 82, 2003 - Issue 2
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Original Articles

Singular Double Porosity Model

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Pages 103-116 | Published online: 09 Sep 2010

  • Allaire , G. 1992 . Homogenization and two-scale Convergence . SIAM J. Math. Anal. , 23 : 1482 – 1518 .
  • Arbogast , T. , Douglas , J. and Hornung , U. 1990 . Derivation of the double porosity model of single phase flow via homogenization theory . SIAM J. Math. Anal. , 21 (4) : 823 – 836 .
  • Barenblatt , G.I. , Zheltov , I.P. and Kochina , N.I. 1960 . Basic concepts of the theory of seepage of homogeneous liquids in fissured rocks . Prikl Math. Mech. , 24 : 852 – 864 .
  • Bear , J. , Tsang , C.F. and de Marsily , G. 1993 . Flow and Contaminant Transport in Fractured Rock , New York - San Francisco - London : Academic Press .
  • Bouchitté , G. and Fragalà , I. 2001 . Homogenization of thin structures by two-scale method with respect to measure . SIAM J. Math. Anal. , 32 (6) : 1198 – 1226 .
  • Bourgeat , A. , Goncharenko , M. , Panfilov , M. and Pankratov , A. 1999 . A general double porosity model . C. R. Acad. Sei. Paris Sér. II , 327 : 1245 – 1250 .
  • Bourgeat , A. , Luckhaus , S. and Mikelic , A. 1996 . Convergence of the homogenization process for a double porosity model of immiscible two phase flow . SIAM J. Appl. Math. , 27 (6) : 1520 – 1543 .
  • Bourgeat , A. , Mikelic , A. and Piatnitski , A.L. 1998 . Random double porosity model . C. R. Acad. Sci. Paris Sér. I Math. , 327 (1) : 99 – 104 .
  • Chechkin , G.A. , Jikov (Zhikov) , V.V. , Lukkassen , D. and Piatnitski , A.L. 2002 . On homogenization on networks and junctions . Asymptotic Analysis , 30 (1) : 61 – 80 .
  • Cioranescu , D. and Paulin , J. Saint Jean . 1999 . Homogenization of reticulated structures. Applied Mathematical Sciences , Volume 136 , Berlin - New York : Springer Verlag .
  • Hornung , U. , ed. 1997 . Homogenization and porous media. IAM , Volume 6 , Berlin New York : Springer Verlag .
  • Jikov (Zhikov) , V.V. 1996 . Connectedness and homogenization . Examples of fractal conductivity. Russian Academy of Sciences, Sbornik: Mathematics , 187 (8) : 1109 – 1147 .
  • Jikov (Zhikov) , V.V. 1998 . Weighted sobolev spaces . Russian Academy of Sciences. Sbornik: Mathematics , 189 (8) : 1139 – 1170 .
  • Jikov (Zhikov) , V.V. 1999 . On the homogenization technique for variational problems . Functional Analysis and its Applications , 33 (1) : 11 – 24 .
  • Jikov (Zhikov) , V.V. 2000 . On one extension and application of the method of two-scale convergence . Russian Academy of Sciences. Sbornik: Mathematics , 191 (7) : 31 – 72 .
  • Nazarov , S.A. 1995 . General averaging procedure for selfadjoint elliptic systems in many-dimensional domains, including thin ones . Algebra and Analysis , 7 (5) : 1 – 92 .
  • St. Petersburg Math. J. , 7 (5) 681 – 748 . English translation
  • Nguetseng , C. 1989 . A general convergence result for a functional related to the theory of homogenization . SIAM J. Math. Anal. , 20 : 608 – 623 .
  • Panassenko , G.P. 2000 . Method of asymptotic partial decomposition of rod structures . International Journal for Computational Civil and Structural Engineering , 1 (2) : 57 – 70 .

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