A stationary flow of fresh and salt groundwater in a heterogeneous coastal aquifer

Si stabilisce l’esistenza e l’unicità di una soluzione monotona per il problema di frontiera libera correlato al flusso stazionare d’acqua dolce e salata intorno ad un acquifero eterogeneo. Si provano la continuità e l’esistenza di un limite asintotico della frontiera libera.

We study a two phase free boundary problem modeling a stationary flow of fresh and salt water through a heterogeneous, horizontal and unbounded two dimensional coastal aquifer. We recall that this problem was studied in [AD1] for the homogeneous case. Existence of a solution was proved together with the continuity of the free boundary (see also [C]) and some qualitative properties. The uniqueness of the solution was left as an open problem. After setting the problem, we establish an existence result for a general matrix permeability. When the permeability depends only on the vertical direction, we prove existence of monotone solutions. For this kind of solutions, we give an asymptotic behavior far away on the left and on the right of the aquifer. We also prove the continuity of the free boundary separating the two fluids. Moreover, we prove uniqueness of these solutions. Finally we study the behavior of the free boundary at the left boundary of its definition interval. The case of a flow governed by a nonlinear Darcy’s law is considered in [CL1] and [CCL].