A non-classical boundary-value problem for the spatial viscous transonic equation

For the three-dimensional viscous transonic equation, a non-classical boundary-value problem with a system of boundary conditions of special form on a one-dimensional manifold is examined. The solution is constructed in the form of a functional series of special form. The convergence of a series which represents the solution is investigated and the well-defined solvability of the problem in the space of analytic functionals Z (R(3)) is proved.