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Existence of solutions to an anisotropic phase-field model
journal contribution
posted on 2023-06-08, 00:10 authored by Erik Burman, Jacques RappazWe 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.
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Publication status
- Published
Journal
Mathematical Methods in the Applied SciencesISSN
0170-4214Publisher
John Wiley and SonsExternal DOI
Issue
13Volume
26Page range
1137-1160Pages
24.0Department affiliated with
- Mathematics Publications
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- No
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- Yes
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2012-02-06Usage metrics
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