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The behavior of the free boundary for the dam problem. (English) Zbl 0521.76092


MSC:

76S05 Flows in porous media; filtration; seepage
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
35R35 Free boundary problems for PDEs
76T99 Multiphase and multicomponent flows
85A35 Statistical astronomy
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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References:

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[7] P. Boieri - F. Gastaldi , Convexity of the free boundary in a filtration problem , J. Differential Equations , to appear. MR 633829 | Zbl 0456.76082 · Zbl 0456.76082 · doi:10.1016/0022-0396(81)90032-2
[8] L.A. Caffarelli - G. Gilardi , Monotonicity of the free boundary in the two-dimensional dam probtem , Ann. Scuola Norm. Sup. Pisa , IV Ser., 7 ( 1980 ), pp. 523 - 537 . Numdam | MR 597551 | Zbl 0513.76090 · Zbl 0513.76090
[9] L.A. Caffarelli - N.M. Riviere , Existence and uniqueness for the problem of filtration through a porous medium , Notices Amer. Math. Soc. , 24 ( 1977 ), p. A-576 .
[10] C.W. Cryer , A survey of steady-state porous flow free boundary problems , M.R.C. Univ. Wisconsin , 1657 ( 1976 ).
[11] A. Friedman - R. Jensen , Convexity of the free boundary in the Stefan problem and in the dam problem , Arch. Rational Mech. Anal. , 67 ( 1977 ), pp. 1 - 24 . MR 473315 | Zbl 0375.35028 · Zbl 0375.35028 · doi:10.1007/BF00280824
[12] G. Gilardi , Studio di una disequazione quasi-variazionale relativa ad un probhema di filtrazione in tre dimensioni , Ann. Mat. Pura Appl. , IV Ser., 113 ( 1977 ), pp. 1 - 17 . MR 513250 | Zbl 0364.76079 · Zbl 0364.76079 · doi:10.1007/BF02418363
[13] J.C. Menendez - M. Chipot , On the dam problem , preprint 1981 . · Zbl 0511.35085
[14] A. Visintin , Existence results for some free boundary filtration problems , Ann. Mat. Pura Appl. , to appear. MR 591561 | Zbl 0445.76078 · Zbl 0445.76078 · doi:10.1007/BF01795398
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