Challal, SLyaghfouri, A2025-03-202025-03-202003-04-17Challal, Samia, and Lyaghfouri, Abdeslem. "On the behavior of the interface separating fresh and salt groundwater in a heterogeneous coastal aquifer.." Electronic Journal of Differential Equations (EJDE) [electronic only] 2003 (2003): Paper No. 44, 27 p., electronic only-Paper No. 44, 27 p., electronic only. <http://eudml.org/doc/123517>.1072-6691https://eudml.org/doc/123517https://hdl.handle.net/10315/42678We 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.enAttribution 4.0 InternationalFresh-salt waterHeterogeneous aquiferNonlinear Darcy's lawMonotone solutionComparison and uniquenessContinuity of the free boundaryLimit behaviorArticle