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• W2055387544 abstract "IN THIS paper we study the flow of an incompressible fluid through a non-homogeneous dam. The problem for the homogeneous, rectangular dam was first considered by Baiocchi [l] and extended to the non-homogeneous case, in which the permeability coefficient has the form k(x, y) = kt(x) . k2(y) by Benci [2] and by Baiocchi and Friedman [3]. The existence and regularity of a solution for the non-homogeneous rectangular dam were proved by Baiocchi [4]. In all of them the so called “Baiocchi transformation” was used. The homogeneous dam problem was also studied using another formulation by Brezis, Kinderlehrer, Stampacchia [5] that have proved the existence and regularity of a solution. In the same setting the uniqueness was studied by Carrillo, Chipot [6]. For the general form of k(x, y), we employ, the same variational formulation as in [5]. In Section 2 we study the equivalence between the physical problem and the variational formulation. The existence of a solution is proved in Section 3 by means of a penalized problem. The proof of the existence of a solution of the latter uses either a fixed point theorem or an existence result for variational inequalities for pseudomonotone operators. The uniqueness is studied under the additional assumption that ak/ay 2 0 (if this condition is not fulfilled some other flow patterns can occur e.g. Alt [7]). The results are extended in Section 5, to the case of the non-homogeneous and anisotropic dam. In Section 6 we consider a layered dam. We prove that the free boundary is a subgraph in each of the layers even if the condition &k/ay 2 0 is satisfied in each layer but not in the whole dam. Some of these results are contained in [8]." @default.
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• W2055387544 date "1985-08-01" @default.
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• W2055387544 title "Incompressible fluid flow through a non- homogeneous and anisotropic dam" @default.
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• W2055387544 doi "https://doi.org/10.1016/0362-546x(85)90019-7" @default.
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