On a uniform approximation of motion by anisotropic curvature by the Allen-Cahn equations
Preprint Series # 738
Giga, Yoshikazu and Ohtsuka, Takeshi and Schaetzle, Reiner On a uniform approximation of motion by anisotropic curvature by the Allen-Cahn equations. (2005);
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.