This article is cited in 1 paper

Transformation of complex velocity area in some problems of filtration in presence of evaporation or infiltration to free surface

E. N. Bereslavskii

St. Petersburg State University of Civil Aviation, 38 Pilotov str., St. Petersburg, 196210 Russia

Abstract: We study a question about possible transformations of complex velocity area in some problems of filtration theory depending on ranges of change constant of conformal mapping, which is contained in forms for mapping function. We examine a linear differential equation of the Fuchsian class, which conform to problem of conformal mapping circular hexagons in polar grid, typical for problems of filtration theory. It has been shown, that at fixing parameter, that determines ratio of circles radii, constituting opposite sides of polygons in the complex flow velocity area, configuration and positional relationship of cutset appreciably depend on not only the properties of the functions, according to which design partial solution of the equation under consideration, but also depend on ranges of change constants of conformal mapping.

Keywords: flow of fluid, filtration, Fuchs differential equations, conformal mappings, area of complex velocity, Jacobi elliptic functions, Theta functions.

UDC: 532.546

Received: 29.04.2015

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:12, 21–27

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