Abstract:
We study a question about possible transformations of complex flow 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, characterizing
ratio of circles radii, constituting opposite sides of polygons in the complex flow velocity
area, configuration of section 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. It turns out that individual ranges of change
these parameters may conform different on their configurations sections, which is demonstration
transformation of filtration fluid flows depending on impact different physical factors and, the
first of all, from evaporating rate or infiltration to the free surface.
Keywords:flow of fluid, filtration, Fuchs differential equations, conformal mappings, area of complex velocity, sections, Jacobi elliptic functions, Theta functions.
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