On the behavior of the interface separating fresh and salt groundwater in a heterogeneous coastal aquifer
Southwest Texas State University, Department of Mathematics
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 g.
Fresh-salt water, Heterogeneous aquifer, Nonlinear Darcy's law, Monotone solutions, Comparison and uniqueness, Continuity of the free boundary, Limit behavior
Challal, S., & Lyaghfouri, A. (2003). On the behavior of the interface separating fresh and salt groundwater in a heterogeneous coastal aquifer. <i>Electronic Journal of Differential Equations, 2003</i>(44), pp. 1-27.