Level-set forced mean curvature flow with the Neumann boundary condition
Level-set forced mean curvature flow with the Neumann boundary condition
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DOI：
10.1016/j.matpur.2022.11.002
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发表时间：
2021-08
期刊：
影响因子：
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通讯作者：
Jiwoong Jang;Dohyun Kwon;Hiroyoshi Mitake;H. Tran
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文献类型：
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作者：
Jiwoong Jang;Dohyun Kwon;Hiroyoshi Mitake;H. Tran
在这里，我们研究了水平集强迫平均曲率流的齐次Neumann边界条件。我们首先表明，解决方案是Lipschitz的时间和局部Lipschitz的空间。然后，在强迫项的一个附加条件下，我们证明了解是全局Lipschitz的。我们得到了在这种情况下的大时间行为的解决方案，并研究在某些特定的情况下的大时间的轮廓。最后，我们给出了两个例子，证明强迫项的附加条件是尖锐的，没有它，解决方案可能不是整体Lipschitz。
Here, we study a level-set forced mean curvature flow with the homogeneous Neumann boundary condition. We first show that the solution is Lipschitz in time and locally Lipschitz in space. Then, under an additional condition on the forcing term, we prove that the solution is globally Lipschitz. We obtain the large time behavior of the solution in this setting and study the large time profile in some specific situations. Finally, we give two examples demonstrating that the additional condition on the forcing term is sharp, and without it, the solution might not be globally Lipschitz.