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

The convergence of solutions of anisotropic Allen–Cahn equations is studied when the interface thickness parameter (denoted by ε) 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...

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Veröffentlicht in:	Interfaces and free boundaries 2006-01, Vol.8 (3), p.317-348
Hauptverfasser:	Giga, Yoshikazu, Ohtsuka, Takeshi, Schätzle, Reiner
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Sprache:	eng
Schlagworte:	Biology and other natural sciences Fluid mechanics Numerical analysis Partial differential equations
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creator	Giga, Yoshikazu Ohtsuka, Takeshi Schätzle, Reiner
description	The convergence of solutions of anisotropic Allen–Cahn equations is studied when the interface thickness parameter (denoted by ε) 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 surface energy density function. As an application the crystalline motion of interfaces is shown to be approximated by the anisotropic Allen–Cahn equations.
doi_str_mv	10.4171/IFB/146
format	Article
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subjects	Biology and other natural sciences Fluid mechanics Numerical analysis Partial differential equations
title	On a uniform approximation of motion by anisotropic curvature by the Allen–Cahn equations
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