论文标题
夹紧曲线的长度保护弹性流的存在和收敛性
Existence and convergence of the length-preserving elastic flow of clamped curves
论文作者
论文摘要
我们研究了固定长度和夹紧边界条件的曲线的演变，该条件通过弹性能的负$ l^2 $ - 速率流动。对于任何初始曲线，仅位于能量空间中，我们就会显示溶液的存在和抛物线平滑。将先前的结果应用于长期存在，并证明lojasiewicz-simon梯度不等式受到约束，我们进一步表明，随着时间趋向于无穷大。
We study the evolution of curves with fixed length and clamped boundary conditions moving by the negative $L^2$-gradient flow of the elastic energy. For any initial curve lying merely in the energy space we show existence and parabolic smoothing of the solution. Applying previous results on long time existence and proving a constrained Lojasiewicz-Simon gradient inequality we furthermore show convergence to a critical point as time tends to infinity.
