The behavior of the free boundary for the dam problem

Hans Wilhelm Alt; Gianni Gilardi

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1982)

  • Volume: 9, Issue: 4, page 571-626
  • ISSN: 0391-173X

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Alt, Hans Wilhelm, and Gilardi, Gianni. "The behavior of the free boundary for the dam problem." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 9.4 (1982): 571-626. <http://eudml.org/doc/83892>.

@article{Alt1982,
author = {Alt, Hans Wilhelm, Gilardi, Gianni},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {flow problems under dam; impervious layers; saturated; unsaturated},
language = {eng},
number = {4},
pages = {571-626},
publisher = {Scuola normale superiore},
title = {The behavior of the free boundary for the dam problem},
url = {http://eudml.org/doc/83892},
volume = {9},
year = {1982},
}

TY - JOUR
AU - Alt, Hans Wilhelm
AU - Gilardi, Gianni
TI - The behavior of the free boundary for the dam problem
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1982
PB - Scuola normale superiore
VL - 9
IS - 4
SP - 571
EP - 626
LA - eng
KW - flow problems under dam; impervious layers; saturated; unsaturated
UR - http://eudml.org/doc/83892
ER -

References

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  1. [1] H.W. Alt, A free boundary problem associated with the flow of ground water, Arch. Rational Mech. Anal., 64 (1977), pp. 111-126. Zbl0371.76079MR428901
  2. [2] H.W. Alt, The fluid flow through porous media. Regularity of the free surface, Manuscripta Math., 21 (1977), pp. 255-272. Zbl0371.76080MR449170
  3. [3] H.W. Alt, Strömungen durch inhomogene poröse Medien mit freiem Rand, J. Reine Angew. Math., 305 (1979), pp. 89-115. Zbl0392.76091MR518852
  4. [4] H.W. Alt, Numerical solution of steady-state porous flow free boundary problems, Numer. Math., 36 (1980), pp. 73-98. Zbl0447.76074MR595808
  5. [5] C. Baiocchi, Su un probtema di frontiera libera connesso a questioni di idraulica, Ann. Mat. Pura Appl., IV Ser., 92 (1972), pp. 107-127. Zbl0258.76069MR408443
  6. [6] C. Baiocchi - A. Capelo, Disequazioni variazionali e quasivariazionali. Applicazioni a probhemi di frontiera (2 Volumes), Pitagora Editrice, Bologna, 1978. 
  7. [7] P. Boieri - F. Gastaldi, Convexity of the free boundary in a filtration problem, J. Differential Equations, to appear. Zbl0456.76082MR633829
  8. [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. Zbl0513.76090MR597551
  9. [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. [10] C.W. Cryer, A survey of steady-state porous flow free boundary problems, M.R.C. Univ. Wisconsin, 1657 (1976). 
  11. [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. Zbl0375.35028MR473315
  12. [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. Zbl0364.76079MR513250
  13. [13] J.C. Menendez - M. Chipot, On the dam problem, preprint 1981. Zbl0511.35085
  14. [14] A. Visintin, Existence results for some free boundary filtration problems, Ann. Mat. Pura Appl., to appear. Zbl0445.76078MR591561

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