We show that the mean curvature flow for a closed and rotationally symmetric surface can be formulated as an evolution problem consisting of an evolution equation for the square of the function whose graph is rotated and two ODEs describing the evolution of the points of the evolving surface that lie on the rotation axis. For the fully nonlinear and degenerate parabolic problem we establish the well-posedness property in the setting of classical solutions. Besides we prove that the problem features the effect of parabolic smoothing.

中文翻译：

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在描述旋转对称封闭面平均曲率流的退化抛物线系统上

我们表明，闭合和旋转对称表面的平均曲率流可以公式化为一个演化问题，该演化问题由函数的平方（其图旋转）和两个ODE组成，这些方程描述了旋转表面的点的演化，位于旋转轴上。对于完全非线性且退化的抛物线问题，我们在经典解的设置中建立了适定性。此外，我们证明了该问题具有抛物线平滑效应。