A generalization of Milne-Thomson theorem for the case of annulus

A closed analytical solution to the problem on 2-D seepage flow with a given main part, $f(z)$, of a desired complex potential in an infinite heterogeneous three-component porous medium is presented. The medium is composed of an isotropic annulus and two other dissimilar components adding annulus up to the whole plane.
New solutions are derived for the cases of arbitrary distribution of singularities of a given main part $f(z)$ including for the cases of singularities at the interface. Besides, the cases involving complex coefficients in the boundary conditions are considered. Four examples, illustrating gotten solutions, are given and corresponding stream lines and equipotential lines are represented.