WIAS Preprint No. 525, (1999)

Global existence of a solution to a phase field model for supercooling



Authors

  • Colli, Pierluigi
  • Frémond, Michel
  • Klein, Olaf
    ORCID: 0000-0002-4142-3603

2010 Mathematics Subject Classification

  • 80A22 35K60 35R35 47H15

Keywords

  • Phase field system, Supercooling, Stefan problem, Global existence result

Abstract

In this work, we will derive a macroscopic model of phase field type for supercooling. The phase transition process is described by the evolution of the temperature and the volume fraction of the liquid phase. This phase field model can also be interpreted as the approximation of some generalized Stefan problem. We will prove the existence of solutions to an initial--boundary value problem for the resulting system by using a time discrete scheme.

Appeared in

  • Nonlinear Anal. Real World Appl, 2 (2001), no. 4, pp. 523-539

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