On a uniform approximation of motion by anisotropic curvature by the Allen-Cahn equations


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Please use this identifier to cite or link to this item:https://doi.org/10.14943/83888

Title:	On a uniform approximation of motion by anisotropic curvature by the Allen-Cahn equations
Authors:	Giga, Yoshikazu Browse this author
	Ohtsuka, Takeshi Browse this author
	Schaetzle, Reiner Browse this author
Keywords:	anisotropic Allen-Cahn equation
	anisotropic mean curvature flow
	viscosity solution
	crystalline curvature flow.
Issue Date:	2005
Publisher:	Department of Mathematics, Hokkaido University
Journal Title:	Hokkaido University Preprint Series in Mathematics
Volume:	738
Start Page:	1
End Page:	36
Abstract:	The convergence of solutions of anisotropic Allen-Cahn equations is studied when the interface thickness parameter(denoted by $\varepsilon$) tends to zero. It is shown that the convergence to a level set solution of the corresponding anisotropic interface equations is uniform with respect to the derivatives of a suface energy density function. As an application a cryatalline motion of interfaces in shown to be approximated by anisotropic Allen-Cahn equations.
Type:	bulletin (article)
URI:	http://hdl.handle.net/2115/69546
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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