A well posed boundary value problem in transonic gas dynamics

Abstract

A new approach considered by Garabedian and Korn (1976) to solve a problem of airfoil design has led to a transonic boundary value problem. It remains to be shown that this problem is well posed. A description is presented of an investigation in which it is shown that a corresponding problem for the Tricomi equation is well posed. The solution to the boundary value problem is characterized, in a unique way, as a sum of two particular solutions. The Poisson formulas for the unit semicircle for the Euler-Poisson-Darboux equation are considered and reflection laws for solutions of the general Euler-Poisson-Darboux equation are established. It is proved that the considered boundary value problem for the case in which the involved function is periodic and continuous is well posed within the specified class of solutions.