Dept. Math, Hokkaido Univ. EPrints Server

Uniqueness and existence of generalized motion for spiral crystal growth

Preprint Series # 872
GOTO, Shun'ichi and NAKAGAWA, Maki and OHTSUKA, Takeshi Uniqueness and existence of generalized motion for spiral crystal growth. (2007);

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Abstract

The uniqueness and existence of generalized solutions of `spiral curves' for the mean curvature flow with driving force is studied by an adapted level set formulation. It is shown that the curves which are given by the level set formulation are unique with respect to initial spiral curves. For given spiral curves the method of a construction of an initial datum of a level set equation is also obtained by constructing a branch of the arguments from the centers of spiral curves, which has discontinuity at the given spiral curves.

Item Type:Preprint
Additional Information:50
Uncontrolled Keywords:level set method viscosity solution mean curvature flow
Subjects:35-xx PARTIAL DIFFERENTIAL EQUATIONS
ID Code:1768