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Weak solutions of a phase-field model for phase change of an alloy with thermal properties

✍ Scribed by José Luiz Boldrini; Gabriela Planas

Publisher
John Wiley and Sons
Year
2002
Tongue
English
Weight
151 KB
Volume
25
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

The phase‐field method provides a mathematical description for free‐boundary problems associated to physical processes with phase transitions. It postulates the existence of a function, called the phase‐field, whose value identifies the phase at a particular point in space and time. The method is particularly suitable for cases with complex growth structures occurring during phase transitions.

The mathematical model studied in this work describes the solidification process occurring in a binary alloy with temperature‐dependent properties. It is based on a highly non‐linear degenerate parabolic system of partial differential equations with three independent variables: phase‐field, solute concentration and temperature.

Existence of weak solutions for this system is obtained via the introduction of a regularized problem, followed by the derivation of suitable estimates and the application of compactness arguments. Copyright © 2002 John Wiley & Sons, Ltd.

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