Fundamental boundary problems of two-dimensional stationary filtration in an anisotropic and inhomogeneous layer of a porous medium (soil formation)- the first and second boundary value problem and the problem of coupling- are formulated and analyzed. A method for solving these problems is proposed. If the anisotropic layer is homogeneous with canonical boundaries (line, ellipse), solutions of the problems have a closed form. In a general case, generalized Cauchy type integral is used. This allows us to reduce the problem to the solution of singular integral equations on the boundaries.
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