We consider a parabolic obstacle problem for Euler’s elastic energy of graphs with fixed ends. We show global existence, well-posedness and subconvergence provided that the obstacle and the initial datum are suitably ‘small’. For symmetric cone obstacles we can improve the subconvergence to convergence. Qualitative aspects such as energy dissipation, coincidence with the obstacle and time regularity are also examined.

中文翻译：

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有障碍物的弹性流：较小的障碍物结果

我们考虑固定端图的Euler弹性能的抛物线障碍问题。如果障碍物和初始基准面适当地“小”，我们将显示全局存在性，适定性和子收敛性。对于对称的圆锥形障碍物，我们可以改善子收敛性。还检查了定性方面，例如能量耗散，障碍物的重合性和时间规律性。