Existence and stability results for the hyperbolic Stefan problem with relaxation

Summary The aim of this paper is to study a phase transition model, based on the Cattaneo-Fourier constitutive law for the heat flux and on a relaxed constitutive law for the phase variable. In turn, the model describes fast processes of melting and crystallization with supercooling and superheating effects. We give existence and stability results for the former phase transition problem. Uniqueness is deduced from the stability result On leave from: Lavrent'ev Institute of Hydrodynamics, 630090 Novosibirsk, Academy of Sciences of Russia, Russia.