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Heat flow with tangent penalisation converging to mean curvature motion

Published online by Cambridge University Press:  14 November 2011

Jian Zhai
Jian Zhai
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo 060, Japan
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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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