The Generalized Radiation Problem and the Euler-Poisson-Darboux Equation

A reformulation of the classical radiation problem for the wave equation leads to a problem for the Euler-Poisson-Darboux equation which includes as a special case the problem of Tricomi, Germain, and Bader. In this last problem which deals with transonic flow arbitrary data are given on the sonic line and prescribed to be zero on a Mach line. The new theory gives the precise conditions under which the radiation problem can be solved and yields new formulas for the solution of the problem for the Tricomi equation.