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.

翻译：双曲曲率流是一种几何演化方程，在平面上可视为曲线缩短流的自然双曲类比。该方程由Gurtin和Podio-Guidugli（1991）提出，用于模拟固-液界面的某些波动现象。我们引入一种半离散有限差分方法来逼近双曲曲率流，并证明了自然离散范数下的误差界。我们还展示了数值模拟结果，包括从光滑严格凸初始数据出发的奇点形成过程。