Undercompressive phase transitions for the model of fluid flows in a nozzle with discontinuous cross-sectional area

Undercompressive phase transitions violating Lax shock inequalities in a model of fluid flows in a nozzle with discontinuous cross-section area are studied. The Riemann problem involving phase transitions is considered. Depending on the choice of admissibility criteria suitable for a specific application, one can obtain a Riemann solver, which may involve nonclassical shock wave. The resonance phenomenon is also observed as multiple shocks waves of the same speed can apparently appear in a single solution. The Riemann problem may admit a unique solution in some region, but may have up to three distinct solutions in other regions.