Weak solution to some Penrose-Fife phase-field systems with temperature-dependent memory
- Colli, Pierluigi
- Sprekels, Jürgen
2010 Mathematics Subject Classification
- 35K50 80A20 80A22
- Penrose-Fife model, phase transitions, memory effects, nonlinear heat conduction, phase-field systems, nonlinear parabolic equations
In this paper a phase-field model of Penrose-Fife type is considered for a diffusive phase transition in a material in which the heat flux is a superposition of two different contributions: one part is proportional to the spatial gradient of the inverse temperature, while the other is of the form of the Gurtin-Pipkin law introduced in the theory of materials with thermal memory. It is shown that an initial-boundary value problem for the resulting state equations has a unique solution, thereby generalizing a number of recent results.
- J. Differ. Equations 142, no. 1, (1998), pp. 54-77