Transonic Evaporation Waves in a Spherically Symmetric Nozzle

This paper studies the liquid to vapor phase transition in a cone shaped nozzle. Using the geometric method presented in [32, 34], we further develop results on subsonic and supersonic evaporation waves in [14] to transonic waves. It is known that transonic waves do not exist if restricted solely to the slow system on the slow manifolds [14]. Thus we consider the existence of transonic waves that include layer solutions of the fast system that cross or connect to the sonic surface. In particular, we are able to show the existence and uniqueness of evaporation waves that cross from supersonic to subsonic regions and evaporation waves that connect from the subsonic region to the sonic surface and then continue onto the supersonic branch via the slow flow.