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Remarks on convergence of the Allen-Cahn equation

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Title: Remarks on convergence of the Allen-Cahn equation
Authors: Tonegawa, Y. Browse this author
Issue Date: Jun-2001
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 531
Start Page: 1
End Page: 18
Abstract: We answer a question posed by Ilmanen on the integrality of varifolds which appear as the singular perturbation limit of the Allen-Cahn equation. We show that the density of the limit measure is integer multiple of the surface constant 1-1,n-1-a.e. for a.e. time. This shows that limit measures obtained via the Allen­Cahn equation and those via Brakke's construction share the same integrality property as well as being weak solutions for the mean curvature flow equation.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69281
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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