On a Penrose-Fife Model with Zero Interfacial Energy Leading to a Phase-field System of Relaxed Stefan Type
- Colli, Pierluigi
- Sprekels, Jürgen
2010 Mathematics Subject Classification
- 35R35 35K50 80A22
- Stefan problems, phase transitions, phase-fieldmodels, singular parabolic systems.
In this paper we study an initial-boundary value Stefan-type problem with phase relaxation where the heat flux is proportional to the gradient of the inverse absolute temperature. This problem arises naturally as limiting case of the Penrose-Fife model for diffusive phase transitions with non-conserved order parameter if the coefficient of the interfacial energy is taken as zero. It is shown that the relaxed Stefan problem admits a weak solution which is obtained as limit of solutions to the Penrose-Fife phase-field equations. For a special boundary condition involving the heat exchange with the surrounding medium, also uniqueness of the solution is proved.
- Ann. Math. Pura Appl. 169 (1995) pp. 269-285