This paper presents a new non-local expanding flow for convex closed curves in the Euclidean plane which increases both the perimeter of the evolving curves and the enclosed area. But the flow expands the evolving curves to a finite circle smoothly if they do not develop singularity during the evolving process. In addition, it is shown that an additional assumption about the initial curve will ensure that the flow exists on the time interval [Formula: see text]. Meanwhile, a numerical experiment reveals that this flow may blow up for some initial convex curves.

中文翻译：

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平面内凸闭合曲线的非局部扩展流

本文提出了一种新的欧几里得平面上凸闭合曲线的非局部扩展流，它增加了演化曲线的周长和封闭区域。但是，如果它们在演化过程中没有发展出奇点，则流动会将演化曲线平滑地扩展为有限圆。此外，还表明，关于初始曲线的附加假设将确保在时间间隔上存在流动[公式：见正文]。同时，数值实验表明，对于一些初始凸曲线，这种流动可能会爆炸。