Asymptotic growth rate of solutions to level-set forced mean curvature flows with evolving spirals

被引:0
作者
Mitake, Hiroyoshi [1 ]
Tran, Hung V. [2 ]
机构
[1] Univ Tokyo, Grad Sch Math Sci, Tokyo, Japan
[2] Univ Wisconsin Madison, Dept Math, Van Vleck hall,480 Lincoln dr, Madison, WI 53706 USA
关键词
EXISTENCE; UNIQUENESS; MOTION; SPEED;
D O I
10.1112/blms.13227
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Here, we study a level-set forced mean curvature flow with evolving spirals and the homogeneous Neumann boundary condition, which appears in a crystal growth model. Under some appropriate conditions on the forcing term, we prove that the solution is globally Lipschitz. We then study the large time average of the solution and deduce the asymptotic growth rate of the crystal. Some large time behavior results of the solution are obtained.
引用
收藏
页码:748 / 770
页数:23
相关论文
共 27 条
[1]   THE GROWTH OF CRYSTALS AND THE EQUILIBRIUM STRUCTURE OF THEIR SURFACES [J].
BURTON, WK ;
CABRERA, N ;
FRANK, FC .
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1951, 243 (866) :299-358
[2]  
CHEN YG, 1991, J DIFFER GEOM, V33, P749, DOI 10.4310/jdg/1214446564
[3]   MOTION OF LEVEL SETS BY MEAN-CURVATURE .1. [J].
EVANS, LC ;
SPRUCK, J .
JOURNAL OF DIFFERENTIAL GEOMETRY, 1991, 33 (03) :635-681
[4]   Steady State and Long Time Convergence of Spirals Moving by Forced Mean Curvature Motion [J].
Forcadel, N. ;
Imbert, C. ;
Monneau, R. .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2015, 40 (06) :1137-1181
[5]   Existence of an Effective Burning Velocity in a Cellular Flow for the Curvature G-Equation Proved Using a Game Analysis [J].
Gao, Hongwei ;
Long, Ziang ;
Xin, Jack ;
Yu, Yifeng .
JOURNAL OF GEOMETRIC ANALYSIS, 2024, 34 (03)
[6]  
Giga Yoshikazu, 2019, Geometric Flows, V4, P9, DOI [10.1515/geofl-2019-0002, 10.1515/geofl-2019-0002]
[7]  
Giga Y, 1999, J DIFFER EQUATIONS, V154, P107
[8]  
Giga Y., 2006, Surface Evolution Equations: A Level Set Approach
[9]  
Giga Y., PROC INT CONG MATH 2, V3, P2305
[10]  
Giga Y, 2021, INDIANA U MATH J, V70, P121