论文标题
平面中离散双曲线曲率流动
Discrete hyperbolic curvature flow in the plane
论文作者
论文摘要
双曲线曲率流是一个几何进化方程，可以将其视为曲线缩短流的天然双曲线类似物。它是由Gurtin和Podio-Guidugli（1991）提出的，以模拟固液界面中的某些波浪现象。我们引入了一种半分化有限差异方法，用于近似双曲线曲率流，并证明自然离散规范的误差界限。我们还提供了数值模拟，包括从平滑的严格凸出初始数据开始的奇异性发作。
Hyperbolic curvature flow is a geometric evolution equation that in the plane can be viewed as the natural hyperbolic analogue of curve shortening flow. It was proposed by Gurtin and Podio-Guidugli (1991) to model certain wave phenomena in solid-liquid interfaces. We introduce a semidiscrete finite difference method for the approximation of hyperbolic curvature flow and prove error bounds for natural discrete norms. We also present numerical simulations, including the onset of singularities starting from smooth strictly convex initial data.
