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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 Rappaz
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.

History

Publication status

  • Published

Journal

Mathematical Methods in the Applied Sciences

ISSN

0170-4214

Publisher

John Wiley and Sons

Issue

13

Volume

26

Page range

1137-1160

Pages

24.0

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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