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Applicable Analysis
An International Journal
Volume 71, 1998 - Issue 1-4
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Original Articles

Passage to the limit in a chain of the muskat problems (I)

Muskat problems (I)

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Pages 91-109 | Received 01 May 1998, Published online: 20 Jan 2011

References

  • Muskat , M. 1934 . Two fluid systems in porous medi, The encroachment of water into an oil sand . Physics , 5 : 250 – 264 .
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  • Oleinik , O. , Primicerio , M. and Radkevich , E. 1993 . Stefan-like problems . Meccanica , 28 ( 6 ) : 129 – 143 .
  • Hillhorst D. Radkevich E. On some smooth approximation for the classical Muskat problem 1998 Proceeding of Moscow Mathematical Society (in Russian)
  • Caginalp , G. 1986 . An analysis of a phase field model of a free boundary . Arch. Mech. Anal , 92 ( 6 ) : 205 – 245 .
  • Caginalp , G. and Fife , P. C. 1987 . Elliptic problems involving phase boundaries satisfying a curvature condition . IMA J. A. Math , 38 ( 6 ) : 195 – 217 .
  • Radkevich , E. V. 1992 . Existence conditions for the classical solution of modified Stefan problem (the Gibbs-Thomson law) . Matem. Sbornik , 183 ( 2 ) : 77 – 101 . (in Russian)
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  • Crowley , A. R. and Ockendon , J. R. 1987 . Modelling mushy regions . AppI. Sci. Res , 44 : 1 – 7 .
  • Meirmanov , A. M. 1981 . An example of nonexistence of a classical solution of the Stefan problem . Soviet Math. Dokl , 23 : 564 – 566 . (Russian)
  • Danilov V. G. Omel'yanov G. A. Radkevich E. V. Hugoniot-type conditions and weak solutions to the phase field system to appear
  • Kametaka Y. Radkevich E. Passage to the limit in a chain of Muskat problems and finger phenomenon Pros. Japan Acad. (to appear)
  • Howison , S. D. , Lacey , A. A. and Ockendon , J. R. 1988 . Hele-Shaw free-boundary problems with suction . Quart. Mech. Appl. Math , 41 : 183 – 193 .

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