Application in Aerohydrodynamics of the Solution of an Inverse Boundary Value Problem for Analytic Functions

Abstract

We consider a modified inverse boundary value problem of aerohydrodynamics in which it is required to find the shape of an airfoil streamlined by a potential flow of an incompressible nonviscous fluid, when the distribution of the velocity potential on one section of the airfoil is given as a function of the abscissa, while, on other sections of the airfoil, as a function of the ordinate of the point. The velocity of the undisturbed flow streamlining the sought-for airfoil is determined in the process of solving the problem. It is shown that, under rather general conditions on the initially set functions, the sought-for contour is closed unlike the inverse problem in the case when, on the unknown contour, the velocity distribution is given as a function of the arc abscissa of the contour point. We also consider the case when, on the entire desired contour, the distribution of the velocity potential is given as a function of one and the same Cartesian coordinate of the contour point.