一个非局部平面凸曲线的发展演化

Evolution of A Nonlocal Planar Convex Curve

针对受外力影响的曲线发展问题,研究了一种新的非局部平面凸曲线的发展演化。在演化过程中,曲线保持凸性,所围区域的面积增大而曲线的长度减少。在Hausdorff测度下,当t趋向于无穷大时,曲线收敛到有限圆。

For the evolution problem of curve influenced by external forces,the evolution of a new nonlocal planar convex curve was studied. The convexity of the evolution curve was kept,and the area of the region surrounded by the evolution curve was increased and the length was decreased in the evolution progress. The curve was converged to finite circle in Hausdorff measure when t approached to infinity.