Geodesic
Axial-symmetry flow through a permeable horizontal layer
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 5 (2005) no. 1, pp. 31-39 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we consider axial-symmetry liquid flow through a porous layer with upper and lower impermeable horizontal boundaries. An injecting well is modeled with prescribed flux on the axis of symmetry. In hydraulic approximation we find similarity solution describing an evolution of free surface. This solution is represented with a series, which coefficients are given by a system of recurrent equations. We analyze the character of free boundary degeneration near by impermeable boundaries. A comparison of a plane flow with the obtained solution had been made. Results are supported by series of calculations. We examine how physical parameters of liquid (density, viscosity) and layer (porosity, permeability) influence on free boundary form. 
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V. V. Molchanov. Axial-symmetry flow through a permeable horizontal layer. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 5 (2005) no. 1, pp. 31-39. http://geodesic.mathdoc.fr/item/VNGU_2005_5_1_a3/

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