Title: Level-set forced mean curvature flow with the Neumann boundary condition Show Chinese title

Title: 带Neumann边界条件的水平集强制平均曲率流

Abstract: 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. Show Chinese abstract

Abstract: 在这里，我们研究带有齐次Neumann边界条件的水平集强制平均曲率流。 我们首先证明解在时间上是Lipschitz连续的，在空间上是局部Lipschitz连续的。 然后，在强制项的一个额外条件下，我们证明解是全局Lipschitz连续的。 我们在这种情况下获得了解的长时间行为，并在一些特定情况下研究了解的长时间轮廓。 最后，我们给出两个例子，说明对强制项的额外条件是精确的，没有这个条件，解可能不是全局Lipschitz连续的。