n this paper a phase-field model of Penrose-Fife type is considered for diffusive phase transitions with conserved order parameter. Different motivations lead to investigate the case when the heat flux is the superposition of two different contributions; one part is the gradient of a function of the absolute temperature θ, behaving like 1/θ as θ approaches to 0 and like -θ as θ ↗ +∞, while the other is given by the Gurtin-Pipkin law introduced in the theory of materials with thermal memory. An existence result for a related initial-boundary value problem is proven. Strengthening some assumptions on the data, the uniqueness of the solution is also achieved.
The conserved Penrose-Fife phase field model with special heat flux laws and memory effects / E. Rocca. - In: JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS. - ISSN 0897-3962. - 14:4(2002), pp. 425-466. [10.1216/jiea/1181074931]
The conserved Penrose-Fife phase field model with special heat flux laws and memory effects
E. Rocca
2002
Abstract
n this paper a phase-field model of Penrose-Fife type is considered for diffusive phase transitions with conserved order parameter. Different motivations lead to investigate the case when the heat flux is the superposition of two different contributions; one part is the gradient of a function of the absolute temperature θ, behaving like 1/θ as θ approaches to 0 and like -θ as θ ↗ +∞, while the other is given by the Gurtin-Pipkin law introduced in the theory of materials with thermal memory. An existence result for a related initial-boundary value problem is proven. Strengthening some assumptions on the data, the uniqueness of the solution is also achieved.File | Dimensione | Formato | |
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