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

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 $g$.

Keywords

• Fresh-salt water
• heterogeneous aquifer
• nonlinear Darcy's law
• monotone solution
• comparison and uniqueness