Modeling of the base of a hydraulic structure with constant flow velocity sections and a curvilinear confining layer

We construct the underground contour of a rectangular subsurface dam, whose corners are rounded in accordance with curves of constant filtration velocity and whose water-permeable base is underlain by a curvilinear confining layer. The latter is assumed to have a horizontal part, while the rest sections are assumed to have a constant flow velocity. We obtain an analytic solution of the corresponding mixed problem of the theory of analytic functions. We adduce results of numerical tests and consider the limit case studied earlier by P. Ya. Polubarinova-Kochina and I. N. Kochina.