Observations on the occurrence of multiple solutions in transonic potential theory (Q1819644)

In recent years it has become apparent that the transonic potential equation does not give a unique solution when shock waves are present in the flow. Most of the studies of this problem are computational in nature. This paper is concerned with an analytic examination of these nonunique solutions. It is concluded that multiple solutions occur when the flow has a supersonic region and that all of the solutions satisfy the usual boundary conditions.