The Riemann Problem and the Existence of Weak Solutions to a System of Mixed-Type in Dynamic Phase Transition

We discuss the Riemann problem and the existence of weak solutions to a dynamic phase transition problem. To estimate the wave strength of outgoing waves containing the phase boundary, we obtain the reflection and transmission coefficients for phase boundary. Then, employing the entropy rate admissibility criterion and the initiation criterion, we prove the existence of global weak solutions via Glimm scheme.