Electron. J. Diff. Eqns.,
Vol. 2003(2003), No. 44, pp. 1-27.
On the behavior of the interface separating fresh
and salt groundwater in a heterogeneous coastal aquifer
Samia Challal & Abdeslem Lyaghfouri
Abstract:
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
of a continuous function. Finally we prove a limit
behavior at the end points of the interval of definition of
.
Submitted December 17, 2002. Published April 17, 2003.
Math Subject Classifications: 35Q35, 35R35, 76S05.
Key Words: Fresh-salt water, heterogeneous aquifer, nonlinear Darcy's law,
monotone solution, comparison and uniqueness,
continuity of the free boundary, limit behavior.
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Samia Challal
King Fahd University of Petroleum and Minerals
P. O. Box 728, Dhahran 31261, Saudi Arabia |
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Abdeslem Lyaghfouri
King Fahd University of Petroleum and Minerals
P. O. Box 728, Dhahran 31261, Saudi Arabia
email: lyaghfo@kfupm.edu.sa |
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