The Riemann problem and the existence of weak solutions to a system of mixed-type in dynamic phase transition
The Riemann problem and the existence of weak solutions to a hyperbolic-elliptic mixed system describing a dynamic phase transition problem are discussed. The system is given by \[ v_t- u_x= 0,\quad u_t- f(v)_x= 0, \] where \(v\), \(u\), and \(f\) are strain, velocity, and stress, respectively. To estimate the wave strength of outgoing waves containing the phase boundary, the reflection and transmission coefficients for the phase boundary are obtained. Employing the entropy rate admissibility criterion and the initiation criterion, the existence of global weak solutions is proved via Glimm scheme.
scientific article; zbMATH DE number 1212363
scientific article