  In this paper, we investigate a model describing induction hardening of
steel. The related system consists of an energy balance, an ODE for the
different phases of steel, and Maxwell's equations in a potential formulation.
The existence of weak entropy solutions is shown by a suitable regularization
and discretization technique. Moreover, we prove the weak-strong uniqueness of
these solutions, i.e., that a weak entropy solutions coincides with a classical
solution emanating form the same initial data as long as the classical one
exists. The weak entropy solution concept has advantages in comparison to the
previously introduced weak solutions, e.g., it allows to include free energy
functions with low regularity properties corresponding to phase transitions.
