The inhomogeneous dam problem with linear Darcy's law and Dirichlet boundary conditions

Mathematical Models and Methods in Applied Sciences

Volumn 6, Issue 8, 1996, Pages 1051-1077

  Lyaghfouri, A ^a  

^a UNIVERSITÉ DE LORRAINE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030352055     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202596000432     Document Type: Article

References (26)

1. R. A. Adams, Sobolev Spaces (Academic Press, 1975).
2. H. W. Alt, The fluid flow through porous media, regularity of the free surface, Manuscripta Math. 21 (1977) 255-272.
3. H. W. Alt, A free boundary problem associated with the flow of ground water, Arch. Rational. Mech. Anal. 64 (1977) 111-126.
4. H. W. Alt, Strömunger durch inhomogene poröse Medien mit freiem Rand, J. Reine Angew. Math. 305 (1979) 89-115.
5. H. W. Alt and G. Gilardi, The behavior of the free boundary for the dam problem, Ann. Sci. Norm. Sup. Pisa IX (1981) 571-626.
6. C. Baiocchi, Su un problema di frontiera libera connesso a questioni di idraulica, Ann. Mat. Pura Appl. 92 (1972) 107-127.
7. C. Baiocchi, Free boundary problems in the theory of fluid flow through porous media, in Proceedings of the International Congress of Mathematicians - Vancouver, (1974), pp. 237-243.
8. C. Baiocchi, Free boundary problems in fluid flows through porous media and variational inequalities, in Free Boundary Problems (Roma, 1980), Vol. 1, pp. 175-191.
9. C. Baiocchi, V. Comincioli, E. Magenes and G. A. Pozzi, Free boundary problems in the theory of fluid flow through porous media: existence and uniqueness theorems, Ann. Mat. Pura Appl. 96 (1973) 1-82.
10. J. Bear and A. Verruijt, Modeling Groundwater Flow and Pollution (D. Reidel, 1992).
11. V. Benci, On a filtration problem through a porous medium, Ann. Mat. Pura Appl. 100 (1974), 191-209.
12. H. Brezis, D. Kinderlehrer and G. Stampacchia: Sur une nouvelle formulation du problm̀e de l'écoulement à travers une digue, C. R. Acd. Sci Paris Serie A287 (1978) 711-714.
13. L. A. Caffarelli and A. Friedman, The dam problem with two layers, Arch. Rational Mech. Anal. 68 (1978) 125-154.
14. L. A. Caffarelli and A. Friedman, Asymptotic estimates for the dam problem with several layers, Indiana Ma. J. 27 (1978), 551-580.
15. L. A. Caffarelli and G. Gilardi, Monotonicity of the free boundary in the two-dimensional dam problem, Ann. Scuola. Norm. Sup. Pisa 7 (1986) 523-537.
16. J. Carrillo and M. Chipot, On the dam problem, J. Differentiel Equations 45 (1982) 234-271.
17. J. Carrillo and M. Chipot, The dam problem with leaky boundary conditions, App. Math. Optim. 28 (1993) 57-85.
18. M. Chipot and A. Lyaghfouri, An existence theorem for an unbounded dam with leaky boundary conditions, in Proc. European Conference on Elliptic and Parabolic Problems, Pitman Research Notes in Mathematics, Vol. 325 (Pitman, 1994), pp. 64-73.
19. M. Chipot and A. Lyaghfouri, The dam problem for nonlinear Darcy's law and leaky boundary conditions, to appear in Math. Methods Appl. Sci.
20. M. Chipot and A. Lyaghfouri, The dam problem with linear Darcy's law and leaky boundary conditions, in preparation.
21. R. Dautray and J. L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques. Tome 2. L'opérateur de Laplace (Masson, 1987).
22. A. Friedman, Variational Principles and Free-Boundary Problems (Robert E. Krieger, 1988).
23. A. Friedman and S.-Y. Huang, The inhomogeneous dam problem with discountinuous permeability, preprint.
24. D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order (Springer-Verlag, 1977).
25. J. F. Rodrigues, On the dam problem with leaky boundary condition, Portugal. Math. 39 (1980) 399-411.
26. R. Stavre and B. Vernescu, Incompressible fluid flow through a nonhomogeneous and anistropic dam, Nonlinear Anal. 9 (1985) 799-810.