Level-set forced mean curvature flow with the Neumann boundary condition

被引：5

作者：

Jang, Jiwoong ^{[1
]}

Kwon, Dohyun ^{[1
]}

Mitake, Hiroyoshi ^{[2
]}

V. Tran, Hung ^{[1
]}

机构：

[1] Univ Wisconsin, Dept Math, Vleck Hall,480 Lincoln Dr, Madison, WI 53706 USA

[2] Univ Tokyo, Grad Sch Math Sci, 3-8-1 Komaba,Meguro Ku, Tokyo 1538914, Japan

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2022年 / 168卷

关键词：

Level-set mean curvature flows; Neumann boundary problem; Global Lipschitz regularity; Large time behavior; The large time profile; ASYMPTOTIC SPEED; TIME BEHAVIOR; HOMOGENIZATION; EXISTENCE; EQUATIONS; EVOLUTION;

D O I：

10.1016/j.matpur.2022.11.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.(c) 2022 Elsevier Masson SAS. All rights reserved.

引用

页码：143 / 167

页数：25