HYPERBOLIC PHASE-CHANGE PROBLEMS IN HEAT-CONDUCTION WITH MEMORY

The aim of this paper is to formulate and study phase transition probl ems in materials with memory, based on the Gurtin-Pipkin constitutive assumption on the heat flux. As different phases are involved, the int ernal energy is allowed to depend on the phase variable (besides the t emperature) and to take its past history into account. By considering the standard equilibrium condition at the interface between two phases , we deal with a hyperbolic Stefan problem reckoning with memory effec ts. Then, substituting this equilibrium condition with a relaxation dy namics, we represent some dissipation phenomena including supercooling or superheating. The application of a fixed point argument helps us t o show the existence and uniqueness of the solution to the latter prob lem (still of hyperbolic type). Hence, by introducing a suitable regul arisation and taking the limit as a kinetic parameter goes to zero, we prove an existence result for the former Stefan problem. Moreover, it s uniqueness is deduced by contradiction.