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Heat flow with tangent penalisation converging to mean curvature motion
Published online by Cambridge University Press: 14 November 2011
Abstract
In this paper, we prove that mean curvature motion can be regarded as the singular limit of the following model:
where ε > 0 is a small parameter and . This model is related to the Landau–Lifshitz equation of ferromagnetism. Local existence of classical solutions of the Dirichlet problem and global existence of the travelling wave solutions are also obtained.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 4 , 1998 , pp. 875 - 894
- Copyright
- Copyright © Royal Society of Edinburgh 1998
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