The Uniqueness of a Transonic Shock in a Nozzle for the 2-D Complete Euler System with the Variable End Perssure

Abstract

In this paper, by use of the methods in [1-3], we establish the uniqueness of a 2-D transonic shock solution in a nozzle when the end pressure in the diverging part of the nozzle lies in an appropriate scope. Especially, we remove the crucial but unnatural assumption in recent references which the transonic shock must be assumed to go through a fixed point in advance.