WIAS Preprint No. 603, (2000)

Existence and approximation of solutions to an anisotropic phase field system of Penrose-Fife type


Authors

  • Klein, Olaf
    ORCID: 0000-0002-4142-3603

2010 Mathematics Subject Classification

  • 65M12 35K50 80A22 35K60 35R35

Keywords

  • Phase-field model, Penrose-Fife model, anisotropie, semidiscretization, convergence

DOI

10.20347/WIAS.PREPRINT.603

Abstract

This paper is concerned with a phase field system of Penrose-Fife type for a non-conserved order parameter χ with a kinetic relaxation coefficient depending on the gradient of χ. This system can be used to model the dendritic solidification of liquids. A time discrete scheme for an initial-boundary value problem tothis system is presented. By proving the convergence of this scheme, the existence of a solution to the problem is shown.

Appeared in

  • Interfaces and Free Boundaries, 4(2002)1, pp. 47-70, with new title:Existence and approximation of solutions to ananisotropic phase field system for the kinetics of phase transition.

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