Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-30T20:19:22.956Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)