A Local Inverse Conical Shock Problem for the Steady Supersonic Potential Flow

Abstract

This paper studies an inverse problem of reconstructing the shape of the circular symmetric cone for the given leading shock front. Assuming that the attack angle is small and that the incoming flow has a large Mach Number, we show that the shape of the cone can be reconstructed near the vertex from the data of the given shock and establish an asymptotic expansion for the velocity and the slope of cone.