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An existence and uniqueness result for a phase-field model of diffusion-induced grain-boundary motion

Published online by Cambridge University Press:  12 July 2007

Klaus Deckelnick  and
Charles M. Elliott
Klaus Deckelnick
Affiliation:
Centre for Mathematical Analysis and its Applications, School of Mathematical Sciences, University of Sussex, Falmer, Brighton BN1 9QH, UK
Charles M. Elliott
Affiliation:
Centre for Mathematical Analysis and its Applications, School of Mathematical Sciences, University of Sussex, Falmer, Brighton BN1 9QH, UK
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Abstract

We consider a phase-field model for diffusion-induced grain boundary motion. The model couples a parabolic variational inequality to a degenerate diffusion equation. Using a regularization technique, we prove an existence theorem for the resulting system. We also obtain a uniqueness result, provided the solution has some additional regularity.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 6 , December 2001 , pp. 1323 - 1344
Copyright
Copyright © Royal Society of Edinburgh 2001

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