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The heterogeneous dam problem with leaky boundary condition
1. | Fields Institute, 222 College Street, Toronto M5T 3J1 |
References:
[1] |
J. Carrillo and M. Chipot, On the dam problem, J. Differential Equations, 45 (1982), 234-271.
doi: doi:10.1016/0022-0396(82)90068-7. |
[2] |
J. Carrillo and M. Chipot, The dam problem with leaky boundary conditions, Applied Mathematics & Optimization, 28 (1993), 57-85.
doi: doi:10.1007/BF01188758. |
[3] |
J. Carrillo and A. Lyaghfouri, The dam problem for nonlinear Darcy's laws and Dirichlet boundary conditions, Annali della Scuola Normale Superiore di Pisa Cl. Sci., 26 (1998), 453-505. |
[4] |
M. Chipot and A. Lyaghfouri, The dam problem for nonlinear Darcy's law and leaky boundary conditions, Mathematical Methods in the Applied Sciences, 20 (1997), 1045-1068.
doi: doi:10.1002/(SICI)1099-1476(199708)20:12<1045::AID-MMA900>3.0.CO;2-3. |
[5] |
M. Chipot and A. Lyaghfouri, The dam problem with linear Darcy's law and leaky boundary conditions, Advances in Differential Equations, 3 (1998), 1-50. |
[6] |
S. Challal and A. Lyaghfouri, A Filtration problem through a heterogeneous porous medium, Interfaces and Free Boundaries, 6 (2004), 55-79.
doi: doi:10.4171/IFB/91. |
[7] |
L. Damascelli, Comparison theorems for some quasilinear degenerate elliptic operators and applications to symmetry and monotonicity results, Ann. Inst. H. Poincaré, 15 (1998), 493-516.
doi: doi:10.1016/S0294-1449(98)80032-2. |
[8] |
E. DiBenedetto, $C^1$ Local regularity of weak solutions of degenerate elliptic equations, Nonlinear Analysis, Theory, Methods & Applications, 7 (1983), 827-850. |
[9] |
A. Friedman and Shav-Yun Huang, The inhomogeneous dam problem with discountinuous permeability, Ann. Scu. Norm. Sup. Pisa, Ser. IV, 14 (1987), 49-77. |
[10] |
A. Lyaghfouri, The inhomogeneous dam problem with linear Darcy's law and Dirichlet boundary conditions, Mathematical Models and Methods in Applied Sciences, 6 (1996), 1051-1077.
doi: doi:10.1142/S0218202596000432. |
[11] |
A. Lyaghfouri, On the uniqueness of the solution of a nonlinear filtration problem through a porous medium, Calculus of Variations and Partial Differential Equations, 6 (1998), 67-94.
doi: doi:10.1007/s005260050082. |
[12] |
A. Lyaghfouri, A unified formulation for the dam problem, Rivista di Matematica della Universit\`a di Parma, 1 (1998), 113-148. |
[13] |
A. Lyaghfouri, A free boundary problem for a fluid flow in a heterogeneous porous medium, Annali dell' Universita di Ferrara-Sez. VII-Sc. Mat., IL (2003), 209-262. |
[14] |
J. F. Rodrigues, On the dam problem with boundary leacky condition, Portugaliae Mathematica, 39 (1980), 399-411. |
[15] |
R. Stavre and B. Vernescu, Incompressible fluid flow through a nonhomogeneous and anisotropic dam, Nonlinear Analysis, 9 (1985), 799-810.
doi: doi:10.1016/0362-546X(85)90019-7. |
show all references
References:
[1] |
J. Carrillo and M. Chipot, On the dam problem, J. Differential Equations, 45 (1982), 234-271.
doi: doi:10.1016/0022-0396(82)90068-7. |
[2] |
J. Carrillo and M. Chipot, The dam problem with leaky boundary conditions, Applied Mathematics & Optimization, 28 (1993), 57-85.
doi: doi:10.1007/BF01188758. |
[3] |
J. Carrillo and A. Lyaghfouri, The dam problem for nonlinear Darcy's laws and Dirichlet boundary conditions, Annali della Scuola Normale Superiore di Pisa Cl. Sci., 26 (1998), 453-505. |
[4] |
M. Chipot and A. Lyaghfouri, The dam problem for nonlinear Darcy's law and leaky boundary conditions, Mathematical Methods in the Applied Sciences, 20 (1997), 1045-1068.
doi: doi:10.1002/(SICI)1099-1476(199708)20:12<1045::AID-MMA900>3.0.CO;2-3. |
[5] |
M. Chipot and A. Lyaghfouri, The dam problem with linear Darcy's law and leaky boundary conditions, Advances in Differential Equations, 3 (1998), 1-50. |
[6] |
S. Challal and A. Lyaghfouri, A Filtration problem through a heterogeneous porous medium, Interfaces and Free Boundaries, 6 (2004), 55-79.
doi: doi:10.4171/IFB/91. |
[7] |
L. Damascelli, Comparison theorems for some quasilinear degenerate elliptic operators and applications to symmetry and monotonicity results, Ann. Inst. H. Poincaré, 15 (1998), 493-516.
doi: doi:10.1016/S0294-1449(98)80032-2. |
[8] |
E. DiBenedetto, $C^1$ Local regularity of weak solutions of degenerate elliptic equations, Nonlinear Analysis, Theory, Methods & Applications, 7 (1983), 827-850. |
[9] |
A. Friedman and Shav-Yun Huang, The inhomogeneous dam problem with discountinuous permeability, Ann. Scu. Norm. Sup. Pisa, Ser. IV, 14 (1987), 49-77. |
[10] |
A. Lyaghfouri, The inhomogeneous dam problem with linear Darcy's law and Dirichlet boundary conditions, Mathematical Models and Methods in Applied Sciences, 6 (1996), 1051-1077.
doi: doi:10.1142/S0218202596000432. |
[11] |
A. Lyaghfouri, On the uniqueness of the solution of a nonlinear filtration problem through a porous medium, Calculus of Variations and Partial Differential Equations, 6 (1998), 67-94.
doi: doi:10.1007/s005260050082. |
[12] |
A. Lyaghfouri, A unified formulation for the dam problem, Rivista di Matematica della Universit\`a di Parma, 1 (1998), 113-148. |
[13] |
A. Lyaghfouri, A free boundary problem for a fluid flow in a heterogeneous porous medium, Annali dell' Universita di Ferrara-Sez. VII-Sc. Mat., IL (2003), 209-262. |
[14] |
J. F. Rodrigues, On the dam problem with boundary leacky condition, Portugaliae Mathematica, 39 (1980), 399-411. |
[15] |
R. Stavre and B. Vernescu, Incompressible fluid flow through a nonhomogeneous and anisotropic dam, Nonlinear Analysis, 9 (1985), 799-810.
doi: doi:10.1016/0362-546X(85)90019-7. |
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