Semidiscrete Elastic Flows of Polygons

Abstract

無中文摘要For N a natural number and any given initial equilateral N-gon, we obtain the long-time existence of smooth solution equilateral N-gons under the semidiscrete second-order evolution equation. Moreover, we conclude the convexity preserving property during the flow, and from taking a convergent subsequence, the asymptotic limit is an equilibrium configuration of the evolution equation.