Study of an inverse boundary value problem of aerohydrodynamics given the value of the forward flow velocity

The inverse boundary value problem of aerohydrodynamics is considered in the new formulation: Find the shape of an airfoil streamlined by a potential flow of an inviscid incompressible fluid under assumption that the velocity potential is given as a function of the abscissa of the profile point, as well as the values of the velocity are available on the leading edge of the airfoil and for the unperturbed flow around the unknown profile. The formulas are derived by which the coordinates of the points of the unknown profile can be calculated and the distribution of the velocity value along the obtained profile can be found. It is shown that, depending on the given value of the velocity of the unperturbed forward flow, the problem is either uniquely solvable or has two solutions with different slope angles of the velocity vector of the forward flow with respect to the real axis.