Existence and convergence of the length-preserving elastic flow of clamped curves
Existence and convergence of the length-preserving elastic flow of clamped curves
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DOI：
10.1007/s00028-024-00988-1
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发表时间：
2024-09-01
影响因子：
1.4
通讯作者：
Spener，Adrian
中科院分区：
文献类型：
--
作者：
Rupp，Fabian;Spener，Adrian
研究了具有固定长度和固定边界条件的曲线在弹性能量负梯度流作用下的演化。对于任何初始曲线只躺在能量空间中，我们显示的存在性和抛物光滑的解决方案。应用以前的结果，长时间存在性和证明一个受约束的Adriojasiewicz-Simon梯度不等式，我们进一步证明了收敛到一个临界点的时间趋于无穷大。
We study the evolution of curves with fixed length and clamped boundary conditions moving by the negative-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 Łojasiewicz–Simon gradient inequality we furthermore show convergence to a critical point as time tends to infinity.