Evolving inextensible and elastic curves with clamped ends under the second-order evolution equation in ℝ2
Chun‐Chi Lin, Yang-Kai Lue · Geometric Flows · 2018
Abstract For any given C 2 -smooth initial open curves with fixed position and fixed tangent at the boundary points, we obtain the long-time existence of smooth solutions under the second-order evolution of plane curves. Moreover, the asymptotic limit of a convergent subsequence is an inextensible elastica.