On the uniqueness of the solution of a unified formulation for the boundary conditions in the dam problem (Q2755661)
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scientific article; zbMATH DE number 1671552
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the uniqueness of the solution of a unified formulation for the boundary conditions in the dam problem |
scientific article; zbMATH DE number 1671552 |
Statements
18 March 2002
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dam problem
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porous medium
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generalized boundary conditions
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Dirichlet conditions
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leaky conditions
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mixed boundary conditions
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regularity of the free boundary
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0.9074154
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0.8994001
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0.8866674
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On the uniqueness of the solution of a unified formulation for the boundary conditions in the dam problem (English)
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The paper deals with a free boundary problem corresponding to a two dimensional steady state model of a dam with a rectangular cross-section. Hence, the equation for the pressure of the fluid in a porous medium is studied in a rectangular domain which is in contact with two reservoirs having different levels. A unified formulation of boundary conditions is considered which includes as particular cases Dirichlet conditions, leaky conditions (describing a flux on the bottoms of the reservoirs supplying the porous medium) and mixed boundary conditions. Various properties of the solution are described, the regularity of the free boundary is studied and the unicity of the solution is proved.
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