Geodesic
On the behavior of the interface separating fresh and salt groundwater in a heterogeneous coastal aquifer
Electronic journal of differential equations, Tome 2003 (2003)
We consider a flow of fresh and salt groundwater in a two-dimensional heterogeneous horizontal aquifer. Assuming the flow governed by a nonlinear Darcy law and the permeability depending only on the vertical coordinate, we show the existence of a unique monotone solution that increases (resp. decreases) with respect to the salt (resp. fresh) water discharge. For this solution we prove that the free boundary is represented by the graph $x=g(z)$ of a continuous function. Finally we prove a limit behavior at the end points of the interval of definition of $g$.
Classification : 35Q35, 35R35, 76S05
Keywords: fresh-salt water, heterogeneous aquifer, nonlinear Darcy's law, monotone solution, comparison and uniqueness, continuity of the free boundary, limit behavior 
@article{EJDE_2003__2003__a184,
     author = {Challal,  Samia and Lyaghfouri,  Abdeslem},
     title = {On the behavior of the interface separating fresh and salt groundwater in a heterogeneous coastal aquifer},
     journal = {Electronic journal of differential equations},
     year = {2003},
     volume = {2003},
     zbl = {1037.35101},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a184/}
}
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%A Lyaghfouri,  Abdeslem
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Challal,  Samia; Lyaghfouri,  Abdeslem. On the behavior of the interface separating fresh and salt groundwater in a heterogeneous coastal aquifer. Electronic journal of differential equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a184/