We consider motion by anisotropic curvature of a network of three curves immersed in the plane meeting at a triple junction and with the other ends fixed. We show existence, uniqueness and regularity of a maximal geometric solution and we prove that, if the maximal time is finite, then either the length of one of the curves goes to zero or the \(L^2\)-norm of the anisotropic curvature blows up.

中文翻译：

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沉浸网络的各向异性曲率流

我们考虑了由三条曲线的网络的各向异性曲率引起的运动，该曲线浸入了在三重接合处相交的平面中，并且其他端部固定。我们显示了最大几何解的存在性，唯一性和规则性，并且证明了，如果最大时间是有限的，那么其中一条曲线的长度将变为零，或者各向异性的\（L ^ 2 \）-范数曲率炸毁。