A well-posedness result for irreversible phase transitions with a nonlinear heat flux law

In this paper, we deal with a PDE system describing a
phase transition problem characterized by irreversible evolution and
ruled by a nonlinear heat flux law. Its derivation comes from the
modelling approach proposed by M. Frémond. Our main
result consists in showing the global-in-time existence and the
uniqueness of the solution of the related initial and boundary value
problem.