We consider an evolving plane curve with two endpoints that can move freely on the x-axis with generating constant contact angles. We discuss the asymptotic behavior of global-in-time solutions when the evolution of this plane curve is governed by the area-preserving curvature flow equation. The main result shows that any moving curve converges to a traveling wave if the moving curve starts from an embedded convex curve and remains bounded in global time.
All Science Journal Classification (ASJC) codes
- Applied Mathematics