Existence of solutions to an anisotropic phase-field model

Burman, Erik and Rappaz, Jacques (2003) Existence of solutions to an anisotropic phase-field model. Mathematical Methods in the Applied Sciences, 26 (13). pp. 1137-1160. ISSN 0170-4214

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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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Erik Burman
Date Deposited: 06 Feb 2012 19:50
Last Modified: 09 May 2012 14:01
URI: http://sro.sussex.ac.uk/id/eprint/22409
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