论文标题
双曲线自由边界问题的曲柄 - 尼古尔森类型最小化方案
A Crank-Nicolson type minimization scheme for a hyperbolic free boundary problem
论文作者
论文摘要
我们通过最大程度地减少曲柄 - 尼科森类型的时间离散功能来考虑双曲线自由边界问题。该功能的特征是它在没有自由边界的情况下享有节能，这是数值计算的重要属性。显示了最小化器的存在和规律性，并得出了能量估计。然后，这些结果用于显示1维环境中自由边界问题的弱解决方案。
We consider a hyperbolic free boundary problem by means of minimizing time discretized functionals of Crank-Nicolson type. The feature of this functional is that it enjoys energy conservation in the absence of free boundaries, which is an essential property for numerical calculations. The existence and regularity of minimizers is shown and an energy estimate is derived. These results are then used to show the existence of a weak solution to the free boundary problem in the 1-dimensional setting.
