WIAS Preprint No. 290, (1996)

Weak solution to some Penrose-Fife phase-field systems with temperature-dependent memory


  • Colli, Pierluigi
    ORCID: 0000-0002-7921-5041
  • Sprekels, Jürgen
    ORCID: 0009-0000-0618-8604

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.

Appeared in

  • J. Differ. Equations 142, no. 1, (1998), pp. 54-77

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