Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 44, pp. 1-27.

Title: On the behavior of the interface separating fresh
       and salt groundwater in a heterogeneous coastal aquifer

Authors: Samia Challal (King Fahd Univ., Dhahran, Saudi Arabia)
 Abdeslem Lyaghfouri (King Fahd Univ., Dhahran, Saudi Arabia)

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 $x=g(z)$ of a continuous function. Finally we prove a limit
  behavior at the end points of the interval of definition of $g$.
 
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.