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

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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
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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