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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