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A free boundary problem arising in oil production. (English) Zbl 0786.76090

Summary: For a stable two-phase free boundary problem arising in oil production, we prove the existence of a weak solution and the continuity of the free boundary.

MSC:

76T99 Multiphase and multicomponent flows
80A22 Stefan problems, phase changes, etc.
35R35 Free boundary problems for PDEs
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References:

[1] Chang, Kung-ching and Jiang, Lishang, ?The free boundary problem of the stationary water cone?,J. Peking Univ., (1)(1978) 1-22.
[2] Lin, Jianchun, Chen, Zhongxiang and Jiang, Lishang, ?The formation of a stable water cone and its control by separate water withdrawal in a producing well?,Acta Mech. Sinica (Beijing),20(3) (1980) 216-223.
[3] Alt, H.W. and Van Duijn, C.J., ?A stationary flow of fresh and salt ground-water in a costal aquifer?,Nonlinear Anal.,14(8) (1990) 625-656. · Zbl 0714.35086 · doi:10.1016/0362-546X(90)90042-F
[4] Gilbarg, D. and Trudinger, N.S.,Elliptic Partial Differential Equations of Second Order (2nd edn), 1983. · Zbl 0562.35001
[5] Caffarelli, L.A., ?A Harnack inequality approach to the regularity of free boundaries?, Part III, Estratto dagli Annali della Scuola Normale Superiore di Pisa Scienze Fisiche e Matematiche; Serie IV, Vol. XV, Fasc. IV (1988).
[6] Miranda, C.,Partial Differential Equations of Elliptic Type (2nd edn), 1970. · Zbl 0198.14101
[7] Alt, H.W., Caffarelli, L.A. and Friedman, A., ?Variational problems with two phases and their free boundaries?,Amer. Math. Soc., No. 2 (1984) 431-461. · Zbl 0844.35137
[8] Alt, H.W., Caffarelli, L.A. and Friedman, A., ?The dam problem with two fluids?,Comm. Pure Appl. Math.,37 (1984) 601-645. · Zbl 0558.76096 · doi:10.1002/cpa.3160370504
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