scholarly journals Global stability of traveling waves for an area preserving curvature flow with contact angle condition

2020 ◽  
Vol 269 (4) ◽  
pp. 3489-3514
Author(s):  
Takashi Kagaya
Keyword(s):  
Contact Angle ◽  
Global Stability ◽  
Traveling Waves ◽  
Curvature Flow ◽  
Angle Condition ◽  
Area Preserving

On an area-preserving inverse curvature flow of convex closed plane curves

2021 ◽  
Vol 280 (8) ◽  
pp. 108931
Author(s):  
Laiyuan Gao ◽  
Shengliang Pan ◽  
Dong-Ho Tsai
Keyword(s):  
Curvature Flow ◽  
Plane Curves ◽  
Area Preserving ◽  
Closed Plane

Mean curvature flow by the Allen–Cahn equation

2015 ◽  
Vol 26 (4) ◽  
pp. 535-559 ◽  
Author(s):  
D. S. LEE ◽  
J. S. KIM
Keyword(s):  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Curve Shortening Flow ◽  
Cahn Equation ◽  
Angle Condition ◽  
Motion By Mean Curvature ◽  
Curve Shortening ◽  
Three Space ◽  
Stable Hybrid

In this paper, we investigate motion by mean curvature using the Allen–Cahn (AC) equation in two and three space dimensions. We use an unconditionally stable hybrid numerical scheme to solve the equation. Numerical experiments demonstrate that we can use the AC equation for applications to motion by mean curvature. We also study the curve-shortening flow with a prescribed contact angle condition.

Evolution of non-simple closed curves in the area-preserving curvature flow

2017 ◽  
Vol 148 (3) ◽  
pp. 659-668 ◽  
Author(s):  
Xiao-Liu Wang ◽  
Wei-Feng Wo ◽  
Ming Yang
Keyword(s):  
Global Solution ◽  
Blow Up ◽  
Curvature Flow ◽  
Convex Curve ◽  
Closed Curves ◽  
Area Preserving ◽  
Locally Convex

The convergence and blow-up results are established for the evolution of non-simple closed curves in an area-preserving curvature flow. It is shown that the global solution starting from a locally convex curve converges to an m-fold circle if the enclosed algebraic area A0 is positive, and evolves into a point if A0 = 0.

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