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Existence of solutions to an anisotropic phase-field model

✍ Scribed by Erik Burman; Jacques Rappaz

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
209 KB
Volume
26
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

We consider an anisotropic phase‐field model for the isothermal solidification of a binary alloy due to Warren–Boettinger ( Acta. Metall. Mater. 1995; 43(2):689). Existence of weak solutions is established under a certain convexity condition on the strongly non‐linear second‐order anisotropic operator and Lipschitz and boundedness assumptions for the non‐linearities. A maximum principle holds that guarantees the existence of a solution under physical assumptions on the non‐linearities. The qualitative properties of the solutions are illustrated by a numerical example. Copyright © 2003 John Wiley & Sons, Ltd.

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