ON THE STABILITY OF STATIONARY LINE AND GRIM REAPER IN PLANAR CURVATURE FLOW

被引：3

作者：

Wang, Xiaoliu ^{[1
]}

Wo, Weifeng ^{[2
]}

机构：

[1] Southeast Univ, Dept Math, Nanjing 210096, Peoples R China

[2] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2011年 / 83卷 / 02期

关键词：

curvature flow; asymptotic behavior; stability; CURVES; EVOLUTION;

D O I：

10.1017/S0004972710001942

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The asymptotic stability of two types of invariant solutions under a curvature flow in the whole plane is studied. First, by extending the work of others, we prove that the stationary line with nonzero slope will attract the graphical curves which surround it. Then a similar property is obtained for the grim reaper.

引用

页码：177 / 188

页数：12

共 50 条

[31] On-line unsupervised planar shape recognition based on curvature functions
Bandera, A
Urdiales, C
Arrebola, F
Sandoval, F
IECON '98 - PROCEEDINGS OF THE 24TH ANNUAL CONFERENCE OF THE IEEE INDUSTRIAL ELECTRONICS SOCIETY, VOLS 1-4, 1998, : 1268 - 1272
[32] Motion by curvature of planar curves with end points moving freely on a line
Xinfu Chen
Jong-Shenq Guo
Mathematische Annalen, 2011, 350 : 277 - 311
[33] FLOW STABILITY AND PRIGOGINE THEOREM FOR THE STATIONARY FLOW OF A VISCOPLASTIC BODY
Solovei, V. D.
JOURNAL OF ENGINEERING PHYSICS AND THERMOPHYSICS, 2011, 84 (06) : 1393 - 1397
[34] Existence and Nonlinear Stability of Stationary Solutions to the Viscous Two-Phase Flow Model in a Half Line
Hai-Liang Li
Shuang Zhao
CommunicationsinMathematicalResearch, 2020, 36 (04) : 423 - 459
[35] Existence and nonlinear stability of stationary solutions to the full two-phase flow model in a half line
Li, Hai-Liang
Zhao, Shuang
APPLIED MATHEMATICS LETTERS, 2021, 116
[36] Existence and nonlinear stability of stationary solutions to the full two-phase flow model in a half line
Li, Hai-Liang
Zhao, Shuang
Applied Mathematics Letters, 2021, 116
[37] MHD STABILITY OF TOROIDAL PLASMA WITH MODULATED CURVATURE PLANAR MAGNETIC AXIS
RIZK, HM
PLASMA PHYSICS AND CONTROLLED FUSION, 1981, 23 (05) : 385 - 397
[38] STATIONARY SOLUTIONS OF AN AREA-PRESERVING CURVATURE FLOW IN AN INHOMOGENEOUS MEDIUM
Lui, R.
Ninomiya, H.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2022, 150 (05) : 2095 - 2105
[39] Stationary Sets and Asymptotic Behavior of the Mean Curvature Flow with Forcing in the Plane
Fusco, Nicola
Julin, Vesa
Morini, Massimiliano
JOURNAL OF GEOMETRIC ANALYSIS, 2022, 32 (02)
[40] Stationary Sets and Asymptotic Behavior of the Mean Curvature Flow with Forcing in the Plane
Nicola Fusco
Vesa Julin
Massimiliano Morini
The Journal of Geometric Analysis, 2022, 32

← 1 2 3 4 5 →