A well posed boundary value problem in transonic gas dynamics

A boundary value problem for the Tricomi equation is studied in connection with transonic gas dynamics. The transformed equation in canonical coordinates is considered in the complex domain of two independent complex variables. A boundary value problem is then set by prescribing the real part of the solution on the boundary of the real unit circle. The Dirichlet problem in the upper unit semicircle with vanishing values of the solution is solved explicitly in terms of the hypergeometric function for the more general Euler-Poisson-Darboux equations. An explicit representation of the solution is also given for a mixed Dirichlet and Neumann problem for the same equation and domain.