An inverse problem for supersonic flow past a curved wedge

Abstract

This paper studies an inverse problem for supersonic potential flow past a curved wedge, in which we design a suitable curved wedge such that the shock produced by the curved wedge can be controlled to the given position. Under suitable conditions, by characteristic method, we prove the existence of the global classical solution to this inverse problem and develop an optimal decay rate on the given shock’s second order derivatives. We finally construct a specific wedge such that the shock generated by the wedge is a convex combined one.