A thermoelastic contact problem with a phase transition

We investigate a thermomechanical contact problem with phase transitions. The system of equations consists of a quasistatic momentum balance and a semilinear energy balance. The phase transition is described by an ordinary differential equation. Different mechanical properties of the respective phases are taken care of by a mixture ansatz. We prove the existence of a weak solution and a uniqueness result, the latter only being valid in one space dimension.