Generalized hodograph transformation and its application to free boundary problems. (Q1852685)

The generalized hodograph transformation is illustrated as a powerful method to solve boundary value problem for p.d.e.'s. Two applications are worked out in details: a) uniform supersonic flow past a non-symmetric cone, b) supersonic flow past a pointed obstacle. The first problem is elliptic and the second is hyperbolic. For problem a) a partial hodograph transformation is used in conjunction with the method of domain decomposition in order to obtain the solution as the limit of a convergent sequence constructed inductively. For problem b), supposing that the body is osculating the tangential cone at the vertex with a sufficiently high order, the solution is obtained as a perturbation of the solution of problem a).