Convergence of diffusion generated motion to motion by mean curvature

被引：13
|
作者：
Swartz, Drew [1 ]
Yip, Nung Kwan [2 ]
机构：
[1] Informat Resources Inc, Chicago, IL USA
[2] Purdue Univ, Dept Math, 150 N Univ St, W Lafayette, IN 47907 USA
来源：
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2017年 / 42卷 / 10期
关键词：
Merriman-Bence-Osher thresholding scheme; motion by mean curvature; APPROXIMATION SCHEME; THRESHOLD DYNAMICS; FLOW; EQUATIONS; PROPAGATION; INTERFACES; SETS;
D O I：
10.1080/03605302.2017.1383418
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We provide a new proof of convergence to motion by mean curvature (MMC) for the Merriman-Bence-Osher thresholding algorithm. The proof is elementary and does not rely on maximum principle for the scheme. The strategy is to construct a natural ansatz of the solution and then estimate the error. The proof thus also provides a convergence rate. Only some weak integrability assumptions of the heat kernel, but not its positivity, is used. Currently the result is proved in the case when smooth and classical solution of MMC exists.
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页码：1598 / 1643
页数：46
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